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• 1.
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
A New Approach for testing Periodicity2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 7, p. 1196-1217Article in journal (Refereed)

This paper describes testing for periodicity in the presence of FD processes. We

propose two approaches for testing the periodicity based on Fisher’s test. The first

one is performed using the periodogram which has been divided into different parts.

The second one is based on the discrete wavelet transform. Properties of the tests are

illustrated by means of Monte Carlo simulations.

• 2.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
Expected and unexpected values of Individual Mahalanobis Distances2017In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 18, p. 8999-9006Article in journal (Refereed)

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.

• 3.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University.
A note on a commonly used ridge regression Monte Carlo design2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 10, p. 2176-2179Article in journal (Refereed)

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.

• 4.
Högskolan i Jönköping.
Robust Testing for Skewness2006In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 36, no 3, p. 485-498Article in journal (Refereed)

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.

• 5.
King Khalid University, Saudi Arabia.
Jönköping University, Sweden. Jönköping University, Sweden. Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University, Sweden.
A Tobit Ridge Regression Estimator2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 1, p. 131-140Article in journal (Refereed)

This article analyzes the effects of multicollienarity on the maximum likelihood (ML) estimator for the Tobit regression model. Furthermore, a ridge regression (RR) estimator is proposed since the mean squared error (MSE) of ML becomes inflated when the regressors are collinear. To investigate the performance of the traditional ML and the RR approaches we use Monte Carlo simulations where the MSE is used as performance criteria. The simulated results indicate that the RR approach should always be preferred to the ML estimation method.

Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University.
Modified Ridge Regression Estimators2013In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 42, no 8, p. 1476-1487Article in journal (Refereed)

Ridge Regression is a variant of ordinary multiple linear regression whose goal is to circumvent the problem of predictors collinearity. It gives-up the Ordinary Least Squares (OLS) estimator as a method for estimating the parameters of the multiple linear regression model . Different methods of specifying the ridge parameter k were proposed and evaluated in terms of Mean Square Error (MSE) by simulation techniques. Comparison is made with other ridge-type estimators evaluated elsewhere. The new estimators of the ridge parameters are shown to have very good MSE properties compared with the other estimators of the ridge parameter and the OLS estimator. Based on our results from the simulation study we may recommend the new ridge parameters to practitioners.

• 7.
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors: An Application to Swedish Immigration Data2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 13, p. 2385-2396Article in journal (Refereed)
• 8.
Jönköping University.
Florida Int Univ, USA. Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University.
Performance of Some Weighted Liu Estimators for Logit Regression Model: An Application to Swedish Accident Data2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 2, p. 363-375Article in journal (Refereed)

In this article, we propose some new estimators for the shrinkage parameter d of the weighted Liu estimator along with the traditional maximum likelihood (ML) estimator for the logit regression model. A simulation study has been conducted to compare the performance of the proposed estimators. The mean squared error is considered as a performance criteria. The average value and standard deviation of the shrinkage parameter d are investigated. In an application, we analyze the effect of usage of cars, motorcycles, and trucks on the probability that pedestrians are getting killed in different counties in Sweden. In the example, the benefits of using the weighted Liu estimator are shown. Both results from the simulation study and the empirical application show that all proposed shrinkage estimators outperform the ML estimator. The proposed D9 estimator performed best and it is recommended for practitioners.

• 9. Månsson, Kristofer
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
On Ridge Parameters in Logistic Regression2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 18, p. 3366-3388Article in journal (Refereed)
• 10.
Jönköping University.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University. Florida International University, USA.
Performance of Some Ridge Regression Estimators for the Multinomial Logit Model2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 12, p. 2795-2804Article in journal (Refereed)

This paper considers several estimators for estimating the ridge parameter  for multinomial logit model based on the work of Khalaf and Shukur (2005), Alkhamisi, Khalaf and Shukur (2006) and  Muniz, Kibria and Shukur (2012). The mean square error (MSE) is considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators.  Based on the simulation study we found that, increasing the correlation between the independent variables and the number of regressors has negative effect on the MSE. However, when the sample size increases the MSE decreases even when the correlation between the independent variables is large. Based on the minimum MSE criterion some useful estimators for estimating the ridge parameter k are recommended for the practitioners.

• 11.
Jönköping University, Sweden.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University, Sweden. Jönköping University, Sweden.
A New Asymmetric Interaction Ridge (AIR) Regression Method2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 3, p. 616-643Article in journal (Refereed)

Despite that interaction terms are standard tools of regression analysis, the side effects of the inclusion of these terms in models estimated by ordinary least squares (OLS) are yet not fully penetrated. The inclusion of interaction effects induces multicollinearity problems since all non-zero values are equal between the interaction term and the regressor. In this article we propose a procedure to remedy this problem by the use of new ridge regression (RR) shrinkage parameters – which we call the asymmetric interaction ridge (AIR) regression method. By means of Monte Carlo simulations we evaluate both OLS and AIR using the mean square error (MSE) performance criterion. The result from the simulation study confirms our hypothesis that AIR always should be preferred to OLS since it has a lower estimated MSE. Moreover, the advantages of our new method are demonstrated in an empirical application where positive asymmetric price transmission effects are exposed for the mortgage interest rates of Handelsbanken Stadshypotek. It is observed that the mortgage interest rates increase more fully and rapidly to an increase in the bank’s borrowing costs than to a decrease. This asymmetry is defined as positive asymmetric price transmission (APT).

• 12.
Jönköping University.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University. Jönköping University.
A New Ridge Regression Causality Test in the Presence of Multicollinearity2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 2, p. 235-248Article in journal (Refereed)

The VAR lag structure applied for the traditional Granger causality (GC) test is always severely affected by multicollinearity due to autocorrelation among the lags. Therefore, as a remedy to this problem we introduce a new Ridge Regression Granger Causality (RRGC) test, which is compared to the GC test by means of Monte Carlo simulations. Based on the simulation study we conclude that the traditional OLS version of the GC test over-rejects the true null hypothesis when there are relatively high (but empirically normal) levels of multicollinearity, while the new RRGC test will remedy or substantially decrease this problem.

• 13.
Lund Universiy.
A consistent estimator of the smoothing operator in the functional Hodrick-Prescott filter2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 12, p. 3029-3042Article in journal (Refereed)

In this paper we consider a version of the functional Hodrick-Prescott ?filter for functional time series. We show that the associated optimal smoothing operator preserves the 'noise-to-signal' structure. Moreover, we propose a consistent estimator of this optimal smoothing operator.

• 14.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Stockholm University, Sweden.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
Mixtures of traces of Wishart and inverse Wishart matrices2019In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed)

Traces of Wishart matrices appear in many applications, for example in finance, discriminant analysis, Mahalanobis distances and angles, loss functions and many more. These applications typically involve mixtures of traces of Wishart and inverse Wishart matrices that are concerned in this paper. Of particular interest are the sampling moments and their limiting joint distribution. The covariance matrix of the marginal positive and negative spectral moments is derived in closed form (covariance matrix of where ). The results are obtained through convenient recursive formulas for and Moreover, we derive an explicit central limit theorem for the scaled vector Y, when and present a simulation study on the convergence to normality and on a skewness measure.

• 15.
On E\big[\prod_{i=0}^k Tr\{W^{m_i}\} \big], where \$W\sim\mathcal{W}_p(I,n)2017In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 6, p. 2990-3005Article in journal (Refereed)

In this paper, we give a general recursive formula for $\small E[\prod_{i=0}^k Tr\{W^{m_i}\}]$, where $\small W \sim \mathscr{W}_p(I,n)$ denotes a real Wishart matrix. Formulas for fixed n, p  are presented as well as asymptotic versions when $\small \frac{n}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c$i.e. when the so called Kolmogorov condition holds. Finally, we show  application of the asymptotic moment relation when deriving moments for the Marchenko-Pastur distribution (free Poisson law). A numerical  illustration using implementation of the main result is also performed.

• 16.
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
Choosing Ridge Parameter for Regression Problems2005In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 34, no 6, p. 1177-1182Article in journal (Refereed)
• 17.
Karolinska Institutet.
Florida International University, USA. Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
Seemingly unrelated regressions with covariance matrix of cross-equation ridge regression residuals2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 20, p. 5029-5053Article in journal (Refereed)

Generalized least squares estimation of a system of seemingly unrelated regressions is usually a two-stage method: (1) estimation of cross-equation covariance matrix from ordinary least squares residuals for transforming data, and (2) application of least squares on transformed data. In presence of multicollinearity problem, conventionally ridge regression is applied at stage 2. We investigate the usage of ridge residuals at stage 1, and show analytically that the covariance matrix based on the least squares residuals does not always result in more efficient estimator. A simulation study and an application to a system of firms' gross investment support our finding.

• 18.
Jönköping University, Sweden.
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University, Sweden.
On the least absolute deviations method for ridge estimation of SURE models2019In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed)

In this paper we examine the application of the Least Absolute Deviations (LAD) method for ridge-type parameter estimation of Seemingly Unrelated Regression Equations (SURE) models. The methodology is aimed to deal with the SURE models with non-Gaussian error terms and highly collinear predictors in each equation. Some biasing parameters used in the literature are taken and the efficiency of both Least Squares (LS) ridge estimation and the LAD ridge estimation of the SURE models, through the Mean Squared Error (MSE) of parameter estimators, is evaluated.

• 19.
Jönköping University.
Linnaeus University, Faculty of Business, Economics and Design, Linnaeus School of Business and Economics.
Modified Ridge Parameters for Seemingly Unrelated Regression Model2012In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 9, p. 1675-1691Article in journal (Refereed)

In this paper, we modify a number of new biased estimators of seemingly unrelated regression (SUR) parameters which are developed by Alkhamisi and Shukur (2008), AS, when the explanatory variables are affected by multicollinearity. Nine estimators of the ridge parameters have been modified and compared in terms of the trace mean squared error (TMSE) and proportion of replications (out of 1,000) for which the SUR version of the generalised least squares (PR) criterion. The results from this extended study are the also compared with those founded by AS. A simulation study has been conducted to compare the performance of the modified estimators of the ridge parameters. The results showed that under certain conditions the performance of the multivariate ridge regression estimators based on SUR ridge RMSmax is superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high the unbiased SUR, estimator produces a smaller TMSEs.

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