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• 1.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Extremal dependency:The GARCH(1,1) model and an Agent based model2013Självständigt arbete på avancerad nivå (magisterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

• 2.
University of Oslo, Norway;University of Biskra, Algeria.
University of Oslo, Norway.
Model uncertainty stochastic mean-field control2019Ingår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, nr 1, s. 36-56Artikel i tidskrift (Refereegranskat)

We consider the problem of optimal control of a mean-field stochasticdifferential equation (SDE) under model uncertainty. The model uncertaintyis represented by ambiguity about the law LðXðtÞÞ of the stateX(t) at time t. For example, it could be the law LPðXðtÞÞ of X(t) withrespect to the given, underlying probability measure P. This is the classicalcase when there is no model uncertainty. But it could also be thelaw LQðXðtÞÞ with respect to some other probability measure Q or,more generally, any random measure lðtÞ on R with total mass 1. Werepresent this model uncertainty control problem as a stochastic differentialgame of a mean-field related type SDE with two players. Thecontrol of one of the players, representing the uncertainty of the lawof the state, is a measure-valued stochastic process lðtÞ and the controlof the other player is a classical real-valued stochastic process u(t).This optimal control problem with respect to random probability processeslðtÞ in a non-Markovian setting is a new type of stochastic controlproblems that has not been studied before. By constructing a newHilbert space M of measures, we obtain a sufficient and a necessarymaximum principles for Nash equilibria for such games in the generalnonzero-sum case, and for saddle points in zero-sum games. As anapplication we find an explicit solution of the problem of optimal consumptionunder model uncertainty of a cash flow described by amean-field related type SDE.

• 3.
Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
Undersökning av metoder för att analysera och modellera efter stora datamaterial, hantering av programmet SPSS samt en studie i Kronoberg läns gymnasieelevers psykiska ohälsa2008Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats

Landstinget i Kronobergs län utförde 2006 en enkätundersökning bland elever i årskurserna 5, 8 och gymnasiets årskurs 2. Datamaterialet för gymnasieeleverna har studerats i detta arbete där den psykiska ohälsan och alkoholkonsumtion varit i fokus.

Det statistiska arbetet är uppdelat i tre delar: Metodbeskrivning, hantering av programmet SPSS samt en undersökning av gymnasieelevers psykiska ohälsa och alkoholkonsumtion. I metodbeskrivningen har metoderna dikotomisering, logistisk regression, Wald, faktorinteraktion och kategorisering beskrivits. För hantering av stora datamaterial samt för att kunna ta fram statistiska samband rörande psykisk ohälsa och alkoholkonsumtion har programmet SPSS använts och illustrerats i arbetet. De förklarande variablerna som varit mest inflytelserika mot den psykiska ohälsan var ’Tycker du att du är frisk?’, ’Har du någonsin använt läkemedel tillsammans med alkohol i berusningssyfte’ samt ’Trivs du med livet?’. När undersökningen för gymnasieelevers alkoholkonsumtion studerades var de gemensamma signifikanta faktorerna för både killar och tjejer ’Skolkar du?’, ’Känner du dig ofta irriterad eller på dåligt humör?’ och ’Har någon vuxen behandlat dig fysiskt illa?’ där samtliga förklarande faktorer bidrog till en ökad sannolikhet att konsumera mycket alkohol. Då undersökning av variabeln symtom, variabeln oro samt deras interaktion studerades för killar respektive för tjejer mot den psykiska ohälsan kunde man se att variabeln symtom för killar var inflytelserik samt interaktionen mellan oro och symtom. För tjejerna var däremot variabeln oro inflytelserik samt variabeln symtom men inte deras interaktion.

• 4.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Forecasting risk premium using wavelet transform2015Ingår i: Festschrift in honor of Professor Ghazi Shukur on the occasion of his 60th birthday / [ed] Thomas Holgersson, Linnaeus University Press, 2015, 1, s. 1-7Kapitel i bok, del av antologi (Övrigt vetenskapligt)
• 5.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University.
Testing for trends and causality in Swedish environmental data, using Wavelet analysis2013Konferensbidrag (Refereegranskat)

This paper utilizes Wavelet based methodology to estimate and test for trends and granger causality in temperature andprecipitation. We use quarterly data from Sweden for the period 1884 up to 2011. The analysis suggests that temperatureand precipitation in Sweden currently have a positive trend in 2011. Thus the recent lower levels of the variables 2009-2010are estimated to be temporary fluctuations or deviations from the trend. Moreover, in the short run there are feedbackeffects between the variables and over longer periods, 4-8 years, temperature granger cause precipitation.

• 6.
Växjö universitet, Fakulteten för humaniora och samhällsvetenskap, Ekonomihögskolan, EHV.
Växjö universitet, Fakulteten för humaniora och samhällsvetenskap, Ekonomihögskolan, EHV. Växjö universitet, Fakulteten för humaniora och samhällsvetenskap, Ekonomihögskolan, EHV.
Wavelet Based Forecasting Approach, with Application2009Ingår i: 2009 International Conference on Financial Theory and Engineering / [ed] Patrick Kellenberger, 2009Konferensbidrag (Refereegranskat)

In this paper we outline a framework for forecasting using maximal overlap discrete wavelet transform (MODWT) based multiresoulution analysis (MRA). This framework has been applied for forecasting the tourism arrival series from Denmark to Norway. We compare forecasted values obtained from modeling the data in the time domain with the forecasted values from the wavelet domain using the traditional Box-Jenkins methodology. In both cases, diagnostic tests have been conducted to insure the specification of the model. The results have shown that the wavelet based forecasts outperforms the traditional Box-Jenkins approach in term of forecasts accuracy.

• 7.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
A Differentiable Approach to Stochastic Differential Equations: the Smoluchowski Limit Revisited2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

In this thesis we generalize results by Smoluchowski [43], Chandrasekhar[6], Kramers, and Nelson [30]. Their aim is to construct Brownian motion as a limit of stochastic processes with differentiable sample paths by exploiting a scaling limit which is a particular type of averaging studied by Papanicolao [35]. Their construction of Brownian motion differs from the one given by Einstein since it constitutes a dynamical theory of Brownian motion. Nelson sets off by studying scaled standard Ornstein-Uhlenbeck processes. Physically these describe classical point particles subject to a deterministic friction and an external random force of White Noise type, which models perpetuous collisions with surrounding(water) molecules. Nelson also studies the case when the particles are subject to an additional deterministic nonlinear force. The present thesis generalizes the work of Chandrasekhar in that it deals with finite dimensional α-stable Lévy processes with 0 < α < 2, and Fractional Brownian motion as driving noises and mathematical techniques like deterministic time change and a Girsanov theorem. We consider uniform convergence almost everywhere and in $L^2$-sense. In order to pursue the limit we multiply all vector fields in the cotangent space by the scaling parameter including the noise. For α-stable Lévy processes this correspondsto scaling the process in the tangent space, $v_{t}$, $t\geq 0$, according to $\beta v_{t}=v_{\beta^{\alpha}t}$. Sending β to infinity means sending time to infinity. In doing so the noise evolves with a different speed in time compared to the component processes. For α≠2, α-stable Lévy processes are of pure jump type, therefore the approximation by processes having continuous sample paths constitutes a valuable mathematical tool. α-stable Lévy processes exceed the class studied by Zhang [46]. In another publication related to this thesis we elaborate on including a mean-field term into the globally Lipschitz continuous nonlinear part of the drift while the noise is Brownian motion, whereas Narita [28] studied a linear dissipation containing a mean-field term. Also the classical McKean-Vlasov model is linear in the mean-field. In a result not included in this thesis the scaling result of Narita [29], which concerns another scaling limit of the tangent space process (velocity) towards a stationary distribution, is generalized to α-stable Lévy processes. The stationary distribution derived by Narita is related to the Boltzmann distribution. In the last part of this thesis we study Fractional Brownian motion with a focus on deriving a scaling limit of Smoluchowski-Kramers type. Since Fractional Brownian motion is no semimartingale the underlying theory of stochastic differential equations is rather involved. We choose to use a Girsanov theorem to approach the scaling limit since the exponent in the Girsanov denvsity does not contain the scaling parameter explicitly. We prove that the Girsanov theorem holds with a linear growth condition alone on the drift for 0 < H < 1, where H is the Hurst parameterof the Fractional Brownian motion.

• 8.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Differentiable Approximation of Diffusion Equations Driven by α-Stable Lévy Noise2013Ingår i: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 27, nr 4, s. 544-552Artikel i tidskrift (Refereegranskat)

Edward Nelson derived Brownian motion from Ornstein-Uhlenbeck theory by a scaling limit. Previously we extended the scaling limit to an Ornstein-Uhlenbeck process driven by an α-stable Lévy process. In this paper we extend the scaling result to α-stable Lévy processes in the presence of a nonlinear drift, an external field of force in physical terms.

• 9.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
Nelson-type Limits for α-Stable Lévy Processes2010Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. Moreover, along with more refined techniques in measure theory and functional analysis more stochastic processes were constructed and studied. Lévy processes, with Brownian motionas a special case, have been of major interest in the recent decades. In addition, Lévy processes include a number of other important processes as special cases like Poisson processes and subordinators. They are also related to stable processes.

In this thesis we generalize a result by S. Chandrasekhar [2] and Edward Nelson who gave a detailed proof of this result in his book in 1967 [12]. In Nelson’s first result standard Ornstein-Uhlenbeck processes are studied. Physically this describes free particles performing a random and irregular movement in water caused by collisions with the water molecules. In a further step he introduces a nonlinear drift in the position variable, i.e. he studies the case when these particles are exposed to an external field of force in physical terms.

In this report, we aim to generalize the result of Edward Nelson to the case of α-stable Lévy processes. In other words we replace the driving noise of a standard Ornstein-Uhlenbeck process by an α-stable Lévy noise and introduce a scaling parameter uniformly in front of all vector fields in the cotangent space, even in front of the noise. This corresponds to time being sent to infinity. With Chandrasekhar’s and Nelson’s choice of the diffusion constant the stationary state of the velocity process (which is approached as time tends to infinity) is the Boltzmann distribution of statistical mechanics.The scaling limits we obtain in the absence and presence of a nonlinear drift term by using the scaling property of the characteristic functions and time change, can be extended to other types of processes rather than α-stable Lévy processes.

In future, we will consider to generalize this one dimensional result to Euclidean space of arbitrary finite dimension. A challenging task is to consider the geodesic flow on the cotangent bundle of a Riemannian manifold with scaled drift and scaled Lévy noise. Geometrically the Ornstein-Uhlenbeck process is defined on the tangent bundle of the real line and the driving Lévy noise is defined on the cotangent space.

• 10.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
Differentiable Approximation by Solutions of Newton Equations Driven by Fractional Brownian Motion.Manuskript (preprint) (Övrigt vetenskapligt)

We derive a Smoluchowski-Kramers type scaling limit for second order stochastic differential equations driven by Fractional Brownian motion.We show a Girsanov theorem for the solution processes with respect to corresponding Fractional Ornstein-Uhlenbeck processes which are Gaussian. This reveals existence of weak solutions as well as a weak scaling limit. Subsequently the results are strengthened.

• 11.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM. Department of Statistics, Warwick University.
Smoluchowski-Kramers Limit for a System Subject to a Mean-Field DriftManuskript (preprint) (Övrigt vetenskapligt)

We establish a scaling limit for autonomous stochastic Newton equations, the solutions are often called nonlinear stochastic oscillators,where the nonlinear drift includes a mean field term of Mckean type and the driving noise is Gaussian. Uniform convergence in $L^{2}$ sense is achieved by applying $L^{p}$-type estimates and the Gronwall Theorem.The approximation is also called Smoluchowski-Kramers limit and is a particular averaging technique studied by Papanicolaou. It reveals an approximation of diffusions with a mean-field contribution in the drift by diffusions with differentiable trajectories.

• 12.
Department of Statistics, University of Warwick.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
A time change method for second order SDEsManuskript (preprint) (Övrigt vetenskapligt)

We study a second order stochastic differential equation which was derived from a non-linear Schrödinger equation with non-linear damping and additive noise to describe the width of related wave solutions. We prove existence of solutions and discuss their long-time behaviour.

• 13.
Warwick University, UK.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
On the collapse of a wave functionsatisfying a damped driven non-linearSchr ̈odinger equationManuskript (preprint) (Övrigt vetenskapligt)

We show that a physically motivated trial solution of a dampeddriven non-linear Schr ̈odinger equation does neither encounter collapse norso-called pseudocollapse although the exponent of the non-linearity is crit-ical. This result sheds new light on the accuracy of numerical solutions tothis problem obtained in an earlier paper where the authors claim pseudo-collapse of the trial solution when the variance of the driving noise is below a certain level.

• 14.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
Edgeworth Expansion and Saddle Point Approximation for Discrete Data with Application to Chance Games2010Självständigt arbete på avancerad nivå (masterexamen), 30 poäng / 45 hpStudentuppsats (Examensarbete)

We investigate mathematical tools, Edgeworth series expansion and the saddle point method, which are approximation techniques that help us to estimate the distribution function for the standardized mean of independent identical distributed random variables where we will take into consideration the lattice case. Later on we will describe one important application for these mathematical tools where game developing companies can use them to reduce the amount of time needed to satisfy their standard requests before they approve any game

• 15.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Mean Field Games for Jump Non-Linear Markov Process2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

The mean-field game theory is the study of strategic decision making in very large populations of weakly interacting individuals. Mean-field games have been an active area of research in the last decade due to its increased significance in many scientific fields. The foundations of mean-field theory go back to the theory of statistical and quantum physics. One may describe mean-field games as a type of stochastic differential game for which the interaction between the players is of mean-field type, i.e the players are coupled via their empirical measure. It was proposed by Larsy and Lions and independently by Huang, Malhame, and Caines. Since then, the mean-field games have become a rapidly growing area of research and has been studied by many researchers. However, most of these studies were dedicated to diffusion-type games. The main purpose of this thesis is to extend the theory of mean-field games to jump case in both discrete and continuous state space. Jump processes are a very important tool in many areas of applications. Specifically, when modeling abrupt events appearing in real life. For instance, financial modeling (option pricing and risk management), networks (electricity and Banks) and statistics (for modeling and analyzing spatial data). The thesis consists of two papers and one technical report which will be submitted soon:

In the first publication, we study the mean-field game in a finite state space where the dynamics of the indistinguishable agents is governed by a controlled continuous time Markov chain. We have studied the control problem for a representative agent in the linear quadratic setting. A dynamic programming approach has been used to drive the Hamilton Jacobi Bellman equation, consequently, the optimal strategy has been achieved. The main result is to show that the individual optimal strategies for the mean-field game system represent 1/N-Nash equilibrium for the approximating system of N agents.

As a second article, we generalize the previous results to agents driven by a non-linear pure jump Markov processes in Euclidean space. Mathematically, this means working with linear operators in Banach spaces adapted to the integro-differential operators of jump type and with non-linear partial differential equations instead of working with linear transformations in Euclidean spaces as in the first work. As a by-product, a generalization for the Koopman operator has been presented. In this setting, we studied the control problem in a more general sense, i.e. the cost function is not necessarily of linear quadratic form. We showed that the resulting unique optimal control is of Lipschitz type. Furthermore, a fixed point argument is presented in order to construct the approximate Nash Equilibrium. In addition, we show that the rate of convergence will be of special order as a result of utilizing a non-linear pure jump Markov process.

In a third paper, we develop our approach to treat a more realistic case from a modelling perspective. In this step, we assume that all players are subject to an additional common noise of Brownian type. We especially study the well-posedness and the regularity for a jump version of the stochastic kinetic equation. Finally, we show that the solution of the master equation, which is a type of second order partial differential equation in the space of probability measures, provides an approximate Nash Equilibrium. This paper, unfortunately, has not been completely finished and it is still in preprint form. Hence, we have decided not to enclose it in the thesis. However, an outlook about the paper will be included.

• 16.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). University of Warwick, UK .
An Approximate Nash Equilibrium for Pure Jump Markov Games of Mean-field-type on Continuous State Space2017Ingår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 89, nr 6-7, s. 967-993Artikel i tidskrift (Refereegranskat)

We investigate mean-field games from the point of view of a large number of indistinguishable players, which eventually converges to infinity. The players are weakly coupled via their empirical measure. The dynamics of the states of the individual players is governed by a non-autonomous pure jump type semi group in a Euclidean space, which is not necessarily smoothing. Investigations are conducted in the framework of non-linear Markovian semi groups. We show that the individual optimal strategy results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players goes to infinity this leads to a jump-type analog of the well-known non-linear McKean–Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The two results combined reveal an epsilon-NashEquilibrium for the N-player games.

• 17.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Warwick University, UK.
An Epsilon Nash Equilibrium For Non-Linear Markov Games of Mean-Field-Type on Finite Spaces2014Ingår i: Communications on Stochastic Analysis, ISSN 0973-9599, Vol. 8, nr 4, s. 449-468Artikel i tidskrift (Refereegranskat)

We investigate mean field games from the point of view of a large number of indistinguishable players which eventually converges to in- finity. The players are weakly coupled via their empirical measure. The dynamics of the individual players is governed by pure jump type propagators over a finite space. Investigations are conducted in the framework of non-linear Markov processes. We show that the individual optimal strategy results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players goes to infinity this leads to a jump-type analog of the well-known non-linear McKean-Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The two results combined reveal a 1 N -Nash Equilibrium for the approximating system of N players.

• 18.
Ibn Tofail University, Morocco.
Ibn Tofail University, Morocco. University of Seville, Spain. Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
A stochastic SIRI epidemic model with Lévy noise2018Ingår i: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 23, nr 9, s. 3645-3661Artikel i tidskrift (Refereegranskat)

Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not acquit permanent immunity but return to infectious class. Such diseases are modeled by SIRI models. In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model with relapse and jumps. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work.

• 19. Bjellerup, Mårten
Högskolan i Jönköping.
A simple multivariate test for asymmetry2009Ingår i: Applied Economics, ISSN 0003-6846, E-ISSN 1466-4283, Vol. 41, nr 11, s. 1405-1416Artikel i tidskrift (Refereegranskat)

Since many macroeconomic models are linear, it is not desirable to use themwith an asymmetric dependent variable. In this article, we formulate aunivariate test for symmetry, based on the third central moment and extendit to a multivariate test; the test does not require modelling and it is robustagainst serial correlation, Autoregressive Conditional Heteroscedasticity(ARCH) and nonnormality. In the empirical application of the test it isfound that orthodox theory seem to be supported; consumption expendi-ture on durable goods is found to be symmetric while consumptionexpenditure on nondurable goods is asymmetric for the USA and the UK,with peaks being higher than troughs are deep. Also, the empiricalimportance of the choice between the univariate and the multivariate testfor possibly correlated series is underscored; the results from the twoapproaches  clearly  differ.  Given  the  widespread  practice  of  usingconsumption expenditure on nondurable goods as the dependent variablein linear models for the USA and the UK, our results might be noteworthy.

• 20.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för naturvetenskap, NV.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för naturvetenskap, NV. Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för naturvetenskap, NV.
PLS-Optimal: A stepwise D-Optimal design based on latent variables2012Ingår i: Journal of Chemical Information and Modeling, ISSN 1549-9596, Vol. 52, nr 4, s. 975-983Artikel i tidskrift (Refereegranskat)

Several applications, such as risk assessment within REACH or drug discovery, require reliable methods for the design of experiments and efficient testing strategies. Keeping the number of experiments as low as possible is important from both a financial and an ethical point of view, as exhaustive testing of compounds requires significant financial resources and animal lives. With a large initial set of compounds, experimental design techniques can be used to select a representative subset for testing. Once measured, these compounds can be used to develop quantitative structure–activity relationship models to predict properties of the remaining compounds. This reduces the required resources and time. D-Optimal design is frequently used to select an optimal set of compounds by analyzing data variance. We developed a new sequential approach to apply a D-Optimal design to latent variables derived from a partial least squares (PLS) model instead of principal components. The stepwise procedure selects a new set of molecules to be measured after each previous measurement cycle. We show that application of the D-Optimal selection generates models with a significantly improved performance on four different data sets with end points relevant for REACH. Compared to those derived from principal components, PLS models derived from the selection on latent variables had a lower root-mean-square error and a higher Q2 and R2. This improvement is statistically significant, especially for the small number of compounds selected.

• 21.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Estimating the Mahalanobis distance in high-dimensional data2013Konferensbidrag (Övrigt vetenskapligt)

The Mahalanobis distance is a fundamental statistic in many fields such as Outlier detection, Normality testing and Cluster analysis. However, the standard estimator developed by Mahalanobis (1936) and Wilks (1963) is not well behaved in cases when the dimension (p) of the parent variable increases proportional to the sample size (n). This case is frequently referred to as Increasing Dimension Asymptotics (IDA). Specifically, the sample covariance matrix on which the Mahalanobis distance depends becomes degenerate under IDA settings, which in turn produce stochastically unstable Mahalanobis distances. This research project consists of several parts. It (a) shows that a previously suggested family of “improved” shrinkage estimators of the covariance matrix produce inoperable Mahalanobis distances, both under classical and increasing dimension asymptotics. It (b) develops a risk function specifically designed to assess the Mahalanobis distance and identifies good estimators thereof and (c) develops a family of resolvent-type estimators of the Mahalanobis distance. This family of estimators is shown to remain well behaved even under IDA settings. Suicient conditions for the proposed estimator to outperform the traditional estimator are also supplied. The proposed estimator is argued to be a useful tool for descriptive statistics, such as Assessment of influential values or Cluster analysis, in cases when the dimension of data is proportional to the sample size.

• 22.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Mahalanobis distances of factor structured data2015Ingår i: Festschrift in honor of Professor Ghazi Shukur on the occasion of his 60th birthday / [ed] Thomas Holgersson, Linnaeus University Press, 2015, 1, s. 126-142Kapitel i bok, del av antologi (Övrigt vetenskapligt)

In this paper, we implement the factor model for deriving the covariance matrix that is used for a Mahalanobis distance. The distributional properties of the new Mahalanobis distances are derived. A general case on contamination effects ofoutliers on Mahalanobis distances from separate parts of the factor model are also investigated. An empirical example indicates the difference between the new proposed separated Mahalanobis distances and the original Mahalanobis distance.

• 23.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Moments, factor scores and limiting distributions of individual Mahalanobis distances2014Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
• 24.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Expected and unexpected values of Individual Mahalanobis Distances2017Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, nr 18, s. 8999-9006Artikel i tidskrift (Refereegranskat)

This paper derives first-order sampling moments of individual Mahalanobis distances (MD) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second order moments are also supplied to give some additional insight to the matter.

• 25.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
On high-dimensional Mahalanobis distance2017Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

The thesis consists of three empirical essays on the topics of self-employment, happiness and international trade.

Essay 1 studies how immigrant self-employment entry is affected by the local business cycle in Sweden. Using the unemployment rate at the local labour market level as a proxy for the local business cycle, our study shows that the self-employment entry behaviour for native men and immigrant men is negatively affected by the unemployment rate, except for immigrants from Middle East. However, such a negative effect is quantitatively weaker among the non-European immigrants. Further, the result shows that immigrants from the Middle East are positively affected by the unemployment rate, meaning they are more likely to be pushed into self-employment in recessions. For women, we also find the unemployment rate has a negative impact on the self-employment decision of native women and immigrant women, except for the Middle East group. However, compared with men, the quantitative size of the unemployment rate effect on self-employment is smaller among women, implying the less important role of business cycle in determining females’ entry into self-employment.

Essay 2 investigates the non-pecuniary return of self-employment in China. The results show that the life satisfaction of self-employed men is significantly higher than that of wage-employed men; the life satisfaction of self-employed women is not statistically significant different from that of wage-employed women. Moreover, we show that the life satisfaction of self-employed men in the informal sector is significantly higher than that of wage-employed men in the formal sector. The life satisfaction of wage-employed men in the informal sector is not significantly different from that of wage-employed men in the formal sector. For women, we find that there is no significant life satisfaction disparity between workers in the formal and informal sector. Finally, our job satisfaction data also concludes that self-employment in China is not inferior to wage employment.

Essay 3 evaluates how Swedish manufacturing employment is affected by the increasing import competition from China. The results show that the growth of manufacturing employment is not statistically significant affected by the increasing import competition from China. Moreover, in general, the increasing import exposure from China does not significantly affect the employment growth of non-manufacturing sector either. Regarding the earnings, the analysis shows that the low wage earners in the manufacturing sector is not significantly affected by the increasing import penetration from China while median and high wage earners are positively affected.

• 26.
École Polytechnique, France.
Technical University of Denmark, Denmark. Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Technical University of Denmark, Denmark.
Detecting Structural Breaks in Time Series via Genetic Algorithms2017Ingår i: Soft Computing - A Fusion of Foundations, Methodologies and Applications, ISSN 1432-7643, E-ISSN 1433-7479, Vol. 21, nr 16, s. 4707-4720Artikel i tidskrift (Refereegranskat)

Detecting structural breaks is an essential task for the statistical analysis of time series, for example, for fitting parametric models to it. In short, structural breaks are points in time at which the behaviour of the time series substantially changes. Typically, no solid background knowledge of the time series under consideration is available. Therefore, a black-box optimization approach is our method of choice for detecting structural breaks. We describe a genetic algorithm framework which easily adapts to a large number of statistical settings. To evaluate the usefulness of different crossover and mutation operations for this problem, we conduct extensive experiments to determine good choices for the parameters and operators of the genetic algorithm. One surprising observation is that use of uniform and one-point crossover together gave significantly better results than using either crossover operator alone. Moreover, we present a specific fitness function which exploits the sparse structure of the break points and which can be evaluated particularly efficiently. The experiments on artificial and real-world time series show that the resulting algorithm detects break points with high precision and is computationally very efficient. A reference implementation with the data used in this paper is available as an applet at the following address: http://​www.​imm.​dtu.​dk/​~pafi/​TSX/​. It has also been implemented as package SBRect for the statistics language R.

• 27.
Technical University of Denmark, Denmark.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
Fast Detection of Structural Breaks2014Ingår i: Proceedings of COMPSTAT 2014, 21th International Conference on Computational Statistics, Geneva, August 19-22, 2014 / [ed] Manfred Gilli, Gil Gonzalez-Rodriguez & Alicia Nieto-Reyes, The International Statistical Institute, 2014, s. 9-16Konferensbidrag (Refereegranskat)

A fundamental task in the analysis of time series is to detect structural breaks. A break indicates a significant change in the behaviour of the series. One method to formalise the notion of a break point, is to fit statistical models piecewise to the series. To find break points, the endpoints of the pieces are varied as is their number. A structural break is indicated by a significant change of the model parameters in adjacent pieces. Both, varying the pieces and repeatedly fitting models to them, are usually computationally very expensive. By combining genetic algorithms with a preprocessing of the time series we design a very fast algorithm for structural break detection. It reduces the time for model-fitting from linear to logarithmic in the length of the series. We show how this method can be used to find structural breaks for time series which are piecewise generated by AR(p)-models. Moreover, we introduce a nonparametric model for which the speed-up can also be achieved. Additionally we briefly present simulation results which demonstrate the manifold applications of these methods. A reference implementation is available at http://www2.imm.dtu.dk/~pafi/StructBreak/index.html

• 28.
University of Leicester, UK.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
A brief introduction to quantum formalism2017Ingår i: The Palgrave Handbook of Quantum Models in Social Science: Applications and Grand Challenges / [ed] Emmanuel Haven, Andrei Khrennikov, Palgrave Macmillan, 2017, s. 1-17Kapitel i bok, del av antologi (Övrigt vetenskapligt)

The authors present briefly the basic notions of the quantum formalism: pure and mixed states; quantum observables; quantum probability; Born’s rule, superposition, and ‘state collapse’; the projection postulate (von Neumann–Lüders postulate); Dirac’s ket and bra-vector notations; elements of quantum information theory and quantum logic; Schrödinger’s and von Neumann’s equations; unitary dynamics; and positive operator valued measures. They also define the basic mathematical notions related to the quantum formalism: Hilbert space; scalar product; norm; Hermitian operator (matrix); projector; and unitary operator and adjoint operator. This chapter may be useful for newcomers to the field, but for those readers who have preliminary knowledge about quantum mechanics (QM) they can proceed directly to advanced chapters.

• 29.
University of Leicester, UK.
Khrennikov, AndreiLinnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
The Palgrave handbook of quantum models in social science: Applications and grand challenges2017Samlingsverk (redaktörskap) (Övrigt vetenskapligt)

It is not intuitive to accept that there exists a link between quantum physical systems and cognitive systems. However, recent research has shown that cognitive systems and collective (social) systems, including biology, exhibit uncertainty which can be successfully modelled with quantum probability. The use of such probability allows for the modelling of situations which typically violate the laws of classical probability. The Palgrave Handbook of Quantum Models in Social Science is is a unique volume that brings together contributions from leading experts on key topics in this new and emerging field. Completely self-contained, it begins with an introductory section which gathers all the fundamental notions required to be able to understand later chapters. The handbook then moves on to address some of the latest research and applications for quantum methods in social science disciplines, including economics, politics and psychology. It begins with the issue of how the quantum mechanical framework can be applied to economics. Chapters devoted to this topic range from how Fisher information can be argued to play a role in economics, to the foundations and application of quantum game theory. The handbook then progresses in considering how belief states can be updated with the theory of quantum measurements (and also with more general methods). The practical use of the Hilbert space (and Fock space) in decision theory is then introduced, and open quantum systems are also considered. The handbook also treats a model of neural oscillators that reproduces some of the features of quantum cognition. Other contributions delve into causal reasoning using quantum Bayes nets and the role of quantum probability in modelling so called affective evaluation. The handbook is rounded off with two chapters which discuss the grand challenges which lie ahead of us. How can the quantum formalism be justified in social science and is the traditional quantum formalism too restrictive? Finally, a question is posed: whether there is a necessary role for quantum mathematical models to go beyond physics. This book will bring the latest and most cutting edge research on quantum theory to social science disciplines. Students and researchers across the discipline, as well as those in the fields of physics and mathematics will welcome this important addition to the literature.

• 30.
Jönköping University.
A Comparative Study of Ten Asymmetry Tests2011Ingår i: Journal of Statistics, ISSN 1684-8403, Vol. 18, s. 10-28Artikel i tidskrift (Refereegranskat)

In this paper, we investigate the properties of some common tests for Asymmetry.The tests are based on Moments, Order Statistics and Empirical CharacteristicFunctions, respectively. These tests have completely different origins, rely ondifferent characterizations of symmetry and have very different size and powerproperties. It is demonstrated that tests based on Empirical CharacteristicFunctions are strongly dependent on the choice of working region and that somepreviously proposed tests may be improved considerably by using Bootstrappedcritical values. It is also concluded that no test is uniformly better than the othersbut that the Empirical Characteristic Function tests have best over-all properties.

• 31.
Högskolan i Jönköping.
A Graphical Technique for Assessing Multivariate Non-normality2006Ingår i: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 21, nr 1, s. 141-149Artikel i tidskrift (Refereegranskat)

In this paper we suggest a simple graphical device for assessing multivariate normality. The method is based on the characteristic that linear combinations of the sample mean and sample covariance matrix are independent if and only if the random variable is normally distributed. We demonstrate the usage of the suggested method and compare it to the classical Q-Q plot by using some multivariate data sets.

• 32.
Högskolan i Jönköping.
A Modified Skewness Measure for Testing Asymmetry2010Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 39, nr 2, s. 335-346Artikel i tidskrift (Refereegranskat)

Statistical practitioners frequently wish to know whether a variable is symmetrically distributed. There are a number of different tests available but the most commonly used one is perhaps that based on the standardized third central moment, as defined by Pearson and Fisher in the early 1900's. While this traditional skewness measure uniquely determines the symmetry of a variable within the Pearson family, it does not uniquely determine symmetry for a general distribution. In this article, we propose a modified version of the classical skewness test which is easy to conduct and consistent against a wide family of asymmetric distributions.

• 33.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University.
A note on a commonly used ridge regression Monte Carlo design2015Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, nr 10, s. 2176-2179Artikel i tidskrift (Refereegranskat)

Ridge estimators are usually examined through Monte Carlo simulations since their properties are difficult to obtain analytically. In this paper we argue that a simulation design commonly used in the literature will give biased results of Monte Carlo simulations in favour of ridge regression over ordinary least square (OLS) estimators. Specifically, it is argued that the properties of ridge estimators that are functions of pdistinct regressor eigenvalues should not be evaluated through Monte Carlo designs using only two distinct eigenvalues.

• 34.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Festschrift in honor of Professor Ghazi Shukur on the occasion of his 60th birthday2015Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
• 35.
Högskolan i Jönköping.
Robust Testing for Skewness2006Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 36, nr 3, s. 485-498Artikel i tidskrift (Refereegranskat)

Statistical analysis frequently involves the problem of assessing distributional properties. This article concerns the problem of testing for skewness of random variables. It is argued that the classical skewness test is not very useful for this purpose, and another approach is suggested that is easy to implement and is also robust to heteroscedasticity. The size, power, and robustness properties of the proposed test is evaluated and compared to the classical skewness test by means of Monte Carlo simulations.

• 36.
Högskolan i Jönköing.
Simulation of Non-normal Auto Correlated Variables2006Ingår i: Journal of Modern Applied Statistical Methods, ISSN 1538-9472, Vol. 5, nr 2, s. 408-416Artikel i tidskrift (Refereegranskat)

All statistical methods rely on assumptions to some extent. Two assumptions frequently met in statistical analyses are those of normal distribution and independence. When examining robustness properties of such assumptions by Monte Carlo simulations it is therefore crucial that the possible effects of autocorrelation and non-normality are not confounded so that their separate effects may be investigated. This article presents a number of non-normal variables with non-confounded autocorrelation, thus allowing the analyst to specify autocorrelation or shape properties while keeping the other effect fixed

• 37.
Högskolan i Jönköping.
Testing for Multivariate Autocorrelation2004Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 31, nr 4, s. 379-395Artikel i tidskrift (Refereegranskat)

This paper concerns the problem of assessing autocorrelation of multivariate (i.e. systemwise) models. It is well known that systemwise diagnostic tests for autocorrelation often suffers from poor small sample properties in the sense that the true size overstates the nominal size. The failure of keeping control of the size usually stems from the fact that the critical values (used to decide the rejection area) originate from the slowly converging asymptotic null distribution. Another drawback of existing tests is that the power may be rather low if the deviation from the null is not symmetrical over the marginal models. In this paper we consider four quite different test techniques for autocorrelation. These are (i) Pillai's trace, (ii) Roy's largest root, (iii) the maximum F-statistic and (iv) the maximum t2 test. We show how to obtain control of the size of the tests, and then examine the true (small sample) size and power properties by means of Monte Carlo simulations.

• 38.
Högskolan i Jönköping.
Högskolan i Jönköping.
An Investigation and Development of Three Estimators of Inverse Covariance Matrices With Applications to the Mahalanobis Distance2010Rapport (Övrigt vetenskapligt)

This paper treats the problem of estimating the inverse covariance matrix in an   increasing   dimension   context.   Specifically,   three   ridge-type   estimators   are considered,  of  which  two  new  are  proposed  by  the  authors  and  one  has  been considered previously. Risk functions for deciding an appropriate value of the ridge coefficient  are  developed  and  the  finite  sample  properties  of  the  estimators  are investigated   in   a   Monte   Carlo   simulation.   Moreover,   risk   functions   for   the Mahalanobis distance are derived which, in turn, leads to three new estimators which has not been considered previously.

Model Based vs. Model Independent Tests for Cross-correlation2010Ingår i: Journal of Modern Applied Statistical Methods, ISSN 1538-9472, Vol. 9, nr 1, s. 75-89Artikel i tidskrift (Refereegranskat)

This article discusses the issue of whether cross correlation should be tested by model dependent or model independent methods. Several different tests are proposed and their main properties are investigated analytically and with simulations. It is argued that model independent tests should be used in applied work.

• 40.
Linnéuniversitetet, Fakultetsnämnden för ekonomi och design, Ekonomihögskolan, ELNU.
Linnéuniversitetet, Fakultetsnämnden för ekonomi och design, Ekonomihögskolan, ELNU.
Three estimators of the Mahalanobis distance in high-dimensional data2012Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 39, nr 12, s. 2713-2720Artikel i tidskrift (Refereegranskat)

This paper treats the problem of estimating the Mahalanobis distance for the purpose of detecting outliers in high-dimensional data. Three ridge-type estimators are proposed and risk functions for deciding an appropriate value of the ridge coefficient are developed. It is argued that one of the ridge estimator has particularly tractable properties, which is demonstrated through outlier analysis of real and simulated data.

• 41.
Jönköping University.
Jönköping University. Jönköping University.
Estimating mean-standard deviation ratios of financial data2012Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 39, nr 3, s. 657-671Artikel i tidskrift (Refereegranskat)

This article treats the problem of linking the relation between excess return and risk of financial assets when the returns follow a factor structure. The authors propose three different estimators and their consistencies are established in cases when the number of assets in the cross-section (n) and the number of observations over time (T) are of comparable size. An empirical investigation is conducted on the Stockholm stock exchange market where the mean-standard deviation ratio is calculated for small- mid- and large cap segments, respectively.

• 42.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University, Sweden.
A risk perspective of estimating portfolio weights of the global minimum-variance portfolio2019Ingår i: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, s. 1-22Artikel i tidskrift (Refereegranskat)

The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n).

• 43.
Högskolan i Jönköping.
Göteborgs universitet.
A Comparison of Conditioned Versus Unconditioned Forecasts of the VAR(1) Process2005Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 34, nr 2, s. 415-427Artikel i tidskrift (Refereegranskat)

The properties of a forecast usually depend upon whether or not the forecast is conditioned on the final period observation. In the case of unconditioned forecasts, it is well known that the point predictions are unbiased. If, on the other hand, the forecast is conditional, then the forecast may be biased. Existing analytical results in literature are insufficient for describing the properties of the conditioned forecast properly, particularly in multivariate models. This article examines some finite sample properties of conditioned forecasts of the VAR(1) process by means of Monte Carlo experiments. We use a number of parameter settings for the VAR(1) process to demonstrate that the forecast bias of the conditioned forecast may be considerable. Hence, unless the analyst has a clear idea of whether the conditioned or unconditioned forecast is relevant for the time series being analyzed, statistical inferences may be seriously erratic.

• 44.
Jönköping University.
Jönköping University.
Assessing Normality of High-Dimensional Data2013Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 42, nr 2, s. 360-369Artikel i tidskrift (Refereegranskat)

The assumption of normality is crucial in many multivariate inference methods and may be even more important when the dimension of data is proportional to the sample size. It is therefore necessary that tests for multivariate non normality remain well behaved in such settings. In this article, we examine the properties of three common moment-based tests for non normality under increasing dimension asymptotics (IDA). It is demonstrated through Monte Carlo simulations that one of the tests is inconsistent under IDA and that one of them stands out as uniformly superior to the other two.

• 45.
Jönköping University.
Jönköping University.
Testing for Autocorrelation in High-dimensional Data2012Rapport (Övrigt vetenskapligt)
• 46.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University.
University of Gothenburg. Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University.
Testing for Panel Unit Roots under General Cross-Sectional Dependence2016Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 45, nr 5, s. 1785-1801Artikel i tidskrift (Refereegranskat)

In this paper we generalize four tests of multivariate linear hypothesis to panel data unit root testing. The test statistics are invariant to certain linear transformations of data and therefore simulated critical values may conveniently be used. It is demonstrated that all four tests remains well behaved in cases of where there are heterogeneous alternatives and cross-correlations between marginal variables. A Monte Carlo simulation is included to compare and contrast the tests with two well-established ones.

• 47.
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS). Jönköping University.
Jönköping University. Jönköping University.
Dummy Variables vs. Category-wise Models2014Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 41, nr 2, s. 233-241Artikel i tidskrift (Refereegranskat)

Empirical research frequently involves regression analysis with binary categorical variables, which are traditionally handled through dummy explanatory variables. This paper argues that separate category-wise models may provide a more logical and comprehensive tool for analysing data with binary categories. Exploring different aspects of both methods, we contrast the two with a Monte Carlo simulation and an empirical example to provide a practical insight.

• 48.
Göteborg University.
Göteborg University.
Some Aspects of Non-Normality Tests in Systems of Regressions Equations2001Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 30, nr 2, s. 291-310Artikel i tidskrift (Refereegranskat)

In this paper, a short background of the Jarque and McKenzie (JM) test for non-normality is given, and the small sample properties of the test is examined in view of robustness, size and power. The investigation has been performed using Monte Carlo simulations where factors like, e.g., the number of equations, nominal sizes, degrees of freedom, have been varied.

Generally, the JM test has shown to have good power properties. The estimated size due to the asymptotic distribution is not very encouraging though. The slow rate of convergence to its asymptotic distribution suggests that empirical critical values should be used in small samples.

In addition, the experiment shows that the properties of the JM test may be disastrous when the disturbances are autocorrelated. Moreover, the simulations show that the distribution of the regressors may also have a substantial impact on the test, and that homogenised OLS residuals should be used when testing for non-normality in small samples.

• 49.
Högskolan i Jönköping.
Högskolan i Jönköping.
Testing for Multivariate Heteroscedasticity2004Ingår i: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 74, nr 12, s. 879-896Artikel i tidskrift (Refereegranskat)

In this article, we propose a testing technique for multivariate heteroscedasticity, which is expressed as a test of linear restrictions in a multivariate regression model. Four test statistics with known asymptotical null distributions are suggested, namely the Wald, Lagrange multiplier (LM), likelihood ratio (LR) and the multivariate Rao F-test. The critical values for the statistics are determined by their asymptotic null distributions, but bootstrapped critical values are also used. The size, power and robustness of the tests are examined in a Monte Carlo experiment. Our main finding is that all the tests limit their nominal sizes asymptotically, but some of them have superior small sample properties. These are the F, LM and bootstrapped versions of Wald and LR tests.

• 50.
Jönköping University.
Jönköping University. Jönköping University.
On regression modelling with dummy variables versus separate regressions per group: comment on Holgersson et al.2016Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 43, nr 8, s. 1564-1565Artikel i tidskrift (Refereegranskat)
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