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Full Description
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 Będlewo, 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.
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 Kozioł, Anuradha Roy, Roman Zmyślony, Ivan Žežula, and Miguel Fonseca).- Testing of multivariate repeated measures data with block exchangeable covariance structure (Ivan Žežula, Daniel Klein, and Anuradha Roy).- On a simplified approach to estimation in experiments with orthogonal block structure (Radosław Kala).- A review of the linear sufficiency and linear prediction sufficiency in the linear model with new observations (Stephen J. Haslett, Jarkko Isotalo, Radosław Kala, Augustyn Markiewicz, and Simo Puntanen).- Linear mixed-effects model using penalized spline based on data transformation methods (Syed Ejaz Ahmed, Dursun Aydın and Ersin Yılmaz).- MMLM meetings - List of Publications.- Index.
