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This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations.
The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Bedlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statisticalscience who are interested in multivariate and mixed linear models.
List of contents
Preface.- Holonomic gradient method for multivariate distribution theory (Akimichi Takemura).- From normality to skewed multivariate distributions: a personal view (Tõnu Kollo).- Multivariate moments in multivariate analysis (Jolanta Pielaszkiewicz and Dietrich von Rosen).- Regularized estimation of covariance structure through quadratic loss function (Defei Zhang, Xiangzhao Cui, Chun Li, Jine Zhao, Li Zeng, and Jianxin Pan).- Separable covariance structure identification for doubly multivariate data (Katarzyna Filipiak, Daniel Klein, and Monika Mokrzycka).- Estimation and testing of the covariance structure of doubly multivariate data (Katarzyna Filipiak and Daniel Klein).- Testing equality of mean vectors with block-circular and block compound-symmetric covariance matrices (Carlos A. Coelho).- Estimation and testing hypotheses in two-level and three-level multivariate data with block compound symmetric covariance structure (Arkadiusz Koziol, Anuradha Roy, Roman Zmyslony, Ivan Zezula, and Miguel Fonseca).- Testing of multivariate repeated measures data with block exchangeable covariance structure (Ivan Zezula, Daniel Klein, and Anuradha Roy).- On a simplified approach to estimation in experiments with orthogonal block structure (Radoslaw Kala).- A review of the linear sufficiency and linear prediction sufficiency in the linear model with new observations (Stephen J. Haslett, Jarkko Isotalo, Radoslaw Kala, Augustyn Markiewicz, and Simo Puntanen).- Linear mixed-effects model using penalized spline based on data transformation methods (Syed Ejaz Ahmed, Dursun Aydin and Ersin Yilmaz).- MMLM meetings - List of Publications.- Index.
About the author
Katarzyna Filipiak is an Associate Professor of Mathematics at the Poznä University of Technology, Poland. She has authored 36 peer-reviewed scientific articles, recently focusing on multivariate statistical models. She acts as a reviewer for many statistical journals, is involved in organizing conferences and currently supervises two PhD students. She is an Associate Editor of Communications in Statistics and the Journal of Multivariate Analysis.
Augustyn Markiewicz is a Professor of Mathematics at the Poznä University of Life Sciences, Poland. He has authored over 60 peer-reviewed articles and has supervised four PhD students. He is an Editorial Board Member of two international journals and has acted as a Guest Editor of several special issues in journals with a high impact factor. He is also involved in organizing international conferences.
Dietrich von Rosen is a Professor of Statistics at the Swedish University of Agricultural Sciences in Uppsala. He has supervised more than 20 PhD students and written more than 130 peer-reviewed articles, both theoretical and applied works. He has written two advanced books in multivariate analysis, the most recent one appearing in 2018. He is the Editor-in-Chief of the Journal of Multivariate Analysis.
