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Holgersson, Thomas
Publications (10 of 38) Show all publications
Pielaszkiewicz, J. M. & Holgersson, T. (2021). Mixtures of traces of Wishart and inverse Wishart matrices. Communications in Statistics - Theory and Methods, 50(21), 5084-5100
Open this publication in new window or tab >>Mixtures of traces of Wishart and inverse Wishart matrices
2021 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 50, no 21, p. 5084-5100Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2021
Keywords
covariance matrix, central limit theorem, eigenvalue distribution, inverse Wishart Matrix, Wishart matrix
National Category
Probability Theory and Statistics Economics and Business
Research subject
Natural Science, Mathematics; Economy
Identifiers
urn:nbn:se:lnu:diva-90504 (URN)10.1080/03610926.2019.1691733 (DOI)000497229800001 ()2-s2.0-85075203911 (Scopus ID)2019 (Local ID)2019 (Archive number)2019 (OAI)
Available from: 2019-12-13 Created: 2019-12-13 Last updated: 2025-05-07Bibliographically approved
Holgersson, T. & Pielaszkiewicz, J. M. (2020). A collection of moments of the Wishart distribution. In: Thomas Holgersson & Martin Singull (Ed.), Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen (pp. 147-162). Springer
Open this publication in new window or tab >>A collection of moments of the Wishart distribution
2020 (English)In: Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen / [ed] Thomas Holgersson & Martin Singull, Springer, 2020, p. 147-162Chapter in book (Refereed)
Abstract [en]

Moments of functions of Wishart distributed matrices appear frequently in multivariate analysis. Although a considerable number of such moments have long been available in the literature, they appear in rather dispersed sources and may sometimes be difficult to locate. This paper presents a collection of moments of the Wishart and inverse Wishart distribution, involving functions such as traces, determinants, Kronecker, and Hadamard products, etc. Moments of factors resulting from decompositions of Wishart matrices are also included.

Place, publisher, year, edition, pages
Springer, 2020
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-98690 (URN)10.1007/978-3-030-56773-6_9 (DOI)2-s2.0-85149271008 (Scopus ID)9783030567729 (ISBN)9783030567736 (ISBN)
Available from: 2020-10-28 Created: 2020-10-28 Last updated: 2025-05-07Bibliographically approved
Holgersson, T., Karlsson, P. S. & Stephan, A. (2020). A risk perspective of estimating portfolio weights of the global minimum-variance portfolio. Paper presented at 104, pages59–80(2020). AStA Advances in Statistical Analysis, 104, 59-80
Open this publication in new window or tab >>A risk perspective of estimating portfolio weights of the global minimum-variance portfolio
2020 (English)In: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 104, p. 59-80Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
Springer, 2020
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-89303 (URN)10.1007/s10182-018-00349-7 (DOI)000515312400004 ()2-s2.0-85061199749 (Scopus ID)
Conference
104, pages59–80(2020)
Available from: 2019-09-26 Created: 2019-09-26 Last updated: 2025-05-23Bibliographically approved
Holgersson, T. & Singull, M. (Eds.). (2020). Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen. Springer
Open this publication in new window or tab >>Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen
2020 (English)Collection (editor) (Refereed)
Abstract [en]

This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as high-dimensional analysis, goodness-of-fit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.

Place, publisher, year, edition, pages
Springer, 2020. p. 373
Keywords
random matrix, regression analysis, time series analysis, high dimensional data, multivariate analysis
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-98688 (URN)10.1007/978-3-030-56773-6 (DOI)2-s2.0-85149339851 (Scopus ID)9783030567729 (ISBN)9783030567736 (ISBN)
Available from: 2020-10-28 Created: 2020-10-28 Last updated: 2023-05-09Bibliographically approved
Holgersson, T. & Singull, M. (2020). Risk and bias in portfolio optimization. In: Thomas Holgersson & Martin Singull (Ed.), Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen (pp. 163-173). Springer
Open this publication in new window or tab >>Risk and bias in portfolio optimization
2020 (English)In: Recent developments in multivariate and random matrix analysis: festschrift in honour of Dietrich von Rosen / [ed] Thomas Holgersson & Martin Singull, Springer, 2020, p. 163-173Chapter in book (Refereed)
Abstract [en]

In this paper we derive weighted squared risk measures for a commonly used Stein-type estimator of the global minimum variance portfolio. The risk functions are conveniently split in terms of variance and squared bias over different weight matrices. It is argued that the common out-of-sample variance criteria should be used with care and that a simple unweighted risk function may be more appropriate.

Place, publisher, year, edition, pages
Springer, 2020
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-98689 (URN)10.1007/978-3-030-56773-6_10 (DOI)2-s2.0-85143860200 (Scopus ID)9783030567729 (ISBN)9783030567736 (ISBN)
Available from: 2020-10-28 Created: 2020-10-28 Last updated: 2023-05-09Bibliographically approved
Dai, D. & Holgersson, T. (2018). High-Dimensional CLTs for Individual Mahalanobis Distances. In: Müjgan Tez & Dietrich von Rosen (Ed.), Müjgan Tez & Dietrich von Rosen (Ed.), Trends and perspectives in linear statistical inference: proceedings of the LINSTAT2016 meeting held 22-25 August 2016 in Istanbul, Turkey. Paper presented at International Conference on Trends and Perspectives in Linear Statistical Inference (LINSTAT2016), Istanbul, Turkey, August 22-25, 2016 (pp. 57-68). Cham, Switzerland: Springer
Open this publication in new window or tab >>High-Dimensional CLTs for Individual Mahalanobis Distances
2018 (English)In: Trends and perspectives in linear statistical inference: proceedings of the LINSTAT2016 meeting held 22-25 August 2016 in Istanbul, Turkey / [ed] Müjgan Tez & Dietrich von Rosen, Cham, Switzerland: Springer, 2018, p. 57-68Conference paper, Published paper (Refereed)
Abstract [en]

Statistical analysis frequently involves methods for reducing high-dimensional data to new variates of lower dimension for the purpose of assessing distributional properties, identification of hidden patterns, for discriminant analysis, etc. In classical multivariate analysis such matters are usually analysed by either using principal components (PC) or the Mahalanobis distance (MD). While the distributional properties of PC’s are fairly well established in high-dimensional cases, no explicit results appear to be available for the MD under such cases. The purpose of this chapter is to bridge that gap by deriving weak limits for the MD in cases where the dimension of the random vector of interest is proportional to the sample size (np-asymptotics). The limiting distributions allow for normality-based inference in cases when the traditional low-dimensional approximations do not apply.

Place, publisher, year, edition, pages
Cham, Switzerland: Springer, 2018
Series
Contributions to Statistics, ISSN 1431-1968
Keywords
Mahalanobis distance, Increasing dimension, Weak convergence, Marchenko-Pastur distribution, Outliers, Pearson family distributions
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-90613 (URN)10.1007/978-3-319-73241-1_4 (DOI)9783319732404 (ISBN)9783319732411 (ISBN)
Conference
International Conference on Trends and Perspectives in Linear Statistical Inference (LINSTAT2016), Istanbul, Turkey, August 22-25, 2016
Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2022-02-22Bibliographically approved
Holgersson, T. & Kekezi, O. (2018). Towards a multivariate innovation index. Economics of Innovation and New Technology (3), 254-272
Open this publication in new window or tab >>Towards a multivariate innovation index
2018 (English)In: Economics of Innovation and New Technology, ISSN 1043-8599, E-ISSN 1476-8364, no 3, p. 254-272Article in journal (Refereed) Published
Abstract [en]

This paper argues that traditional measures of innovation as a univariate phenomenon may not be dynamic enough to adequately describe the complex nature of innovation. Consequently, the purpose is to develop a multidimensional index of innovation that is able to reflect innovation enablers and outputs. The index may then be used (i) to assess and quantify temporal changes of innovation, (ii) to describe regional differences and similarities of innovation, and (iii) serve as exogenous variables to analyze the importance of innovation for other economic phenomena. Our index is defined in a four-dimensional space of orthogonal axes. An empirical case study is used for demonstration of the index, where 44 variables are collected for all municipalities in Sweden. The index spanning the four-dimensional innovation comprises size, accessibility, firm performance, and agglomeration. The proposed index offers a new way of defining and analyzing innovation and should have a wide range of important applications in a world where innovation is receiving a great deal of recognition.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Regional innovation, Multivariate index, Factor analysis
National Category
Economics
Research subject
Economy, Economics
Identifiers
urn:nbn:se:lnu:diva-64888 (URN)10.1080/10438599.2017.1331788 (DOI)000438041100004 ()2-s2.0-85020272337 (Scopus ID)
Available from: 2017-06-07 Created: 2017-06-07 Last updated: 2019-12-16Bibliographically approved
Dai, D., Holgersson, T. & Karlsson, P. S. (2017). Expected and unexpected values of Individual Mahalanobis Distances. Communications in Statistics - Theory and Methods, 46(18), 8999-9006
Open this publication in new window or tab >>Expected and unexpected values of Individual Mahalanobis Distances
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 18, p. 8999-9006Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keywords
Increasing dimension, Mahalanobis distance, Expected values, Inverse covariance matrix
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
urn:nbn:se:lnu:diva-55787 (URN)10.1080/03610926.2016.1200096 (DOI)000407584900013 ()2-s2.0-85019639941 (Scopus ID)
Available from: 2016-08-26 Created: 2016-08-26 Last updated: 2022-02-22Bibliographically approved
Holgersson, T., Karlsson, P. S. & Stephan, A. (2016). A risk perspective of estimating portfolio weights of the Global Minimum Variance portfolio. In: Presented at Statistischen Woche 2016, Augsburg, Germany, September 13-16, 2016: . Paper presented at Statistischen Woche 2016, Augsburg, Germany, September 13-16, 2016.
Open this publication in new window or tab >>A risk perspective of estimating portfolio weights of the Global Minimum Variance portfolio
2016 (English)In: Presented at Statistischen Woche 2016, Augsburg, Germany, September 13-16, 2016, 2016Conference paper, Oral presentation with published abstract (Other academic)
Abstract [en]

The problem of how to maximize the return on a given portfolio of assets within the theory of Markowitz has been given considerable attention in the literature and improvements of standard methods continues to progress. Recent developments, often based on Stein estimators or other regularized estimators, usually focus on settings when the numbers of assets (say p) is close to the number of observations (n) since this is the scenario met in most real applications. Before any specific method is applied investors would want to know the basic properties and the relative performance of them. The performance of any estimation method, however, depends on which quality criterea of judgement is being used. Proposed methods may be optimal with respect to precision of the parameters involved in the portfolio procedure, on the proximity between estimated vs true global minimum variance portfolio (GMVP) weights, on the out-of-sample performance etc. Moreover, regularized estimators are often associated with very complicated or even unknown sampling distributions, which in turn complicate statistical inference drastically. The extent to which a method allows for statistical inference therefore also becomes an important matter when judging the properties of a data driven GMVP estimator. In this paper we give an in-depth discussion of risk critereas and their impact on GMVP optimization. A Monte Carlo simulation investigating the properties of some common estimators, including a new one proposed by the authors, with respect to several quality critereas is included to compare and contrast recent proposals. An empirical study is also included using Stockholm stock exchange data. 

National Category
Economics and Business
Research subject
Economy
Identifiers
urn:nbn:se:lnu:diva-58609 (URN)
Conference
Statistischen Woche 2016, Augsburg, Germany, September 13-16, 2016
Available from: 2016-11-30 Created: 2016-11-30 Last updated: 2025-05-23Bibliographically approved
Holgersson, T. (2016). How to formulate relevant and assessable learning outcomes in statistics. Creative Education, 7(4), 669-675
Open this publication in new window or tab >>How to formulate relevant and assessable learning outcomes in statistics
2016 (English)In: Creative Education, ISSN 2151-4755, E-ISSN 2151-4771, Vol. 7, no 4, p. 669-675Article in journal (Refereed) Published
Abstract [en]

Course syllabuses, outlines or similar academic documents specifying the content of a course will often be a helpful tool both for teachers and students to grasp the content and purpose of a course. In many cases, however, the compilation of such documents is a painstaking process for the educator designing it, and is a task that many teachers will shun. In this paper we propose a fairly simple pedagogical model for designing specific learning outcomes that the students are expected to attain after completion of a course.

Place, publisher, year, edition, pages
Scientific Research Publishing, 2016
Keywords
Learning Assessment, Course Syllabus, Statistics
National Category
Pedagogy
Research subject
Pedagogics and Educational Sciences
Identifiers
urn:nbn:se:lnu:diva-51317 (URN)10.4236/ce.2016.74070 (DOI)
Available from: 2016-03-24 Created: 2016-03-24 Last updated: 2017-11-30Bibliographically approved
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