Advanced Multivariate Statistics with Matrices by Tõnu KolloAdvanced Multivariate Statistics with Matrices by Tõnu Kollo

Advanced Multivariate Statistics with Matrices

byTõnu Kollo, D. von Rosen

Paperback | January 22, 2011

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This book presents the authors' personal selection of topics in multivariate statistical analysis with emphasis on tools and techniques. Topics included range from definitions of multivariate moments, multivariate distributions, asymptotic distributions of commonly used statistics and density approximations to a modern treatment of multivariate linear models. The theory used is based on matrix algebra and linear spaces and applies lattice theory in a systematic way. Many of the results are obtained by utilizing matrix derivatives which in turn are built up from the Kronecker product and vec-operator. The matrix normal, Wishart and elliptical distributions are studied in detail. In particular, several moment relations are given. Together with the derivatives of density functions, formulae are presented for density approximations, generalizing classical Edgeworth expansions. The asymptotic distributions of many commonly used statistics are also derived. In the final part of the book the Growth Curve model and its various extensions are studied.The book will be of particular interest to researchers but could also be appropriate as a text-book for graduate courses on multivariate analysis or matrix algebra.
Title:Advanced Multivariate Statistics with MatricesFormat:PaperbackDimensions:506 pagesPublished:January 22, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048168597

ISBN - 13:9789048168590

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Table of Contents

From the contentsPreface.- Introduction.- 1. Basic Matrix Theory And Linear.- 2. Multivariate Distributions.- 3. Distribution Expansions.- 4. Multivariate Linear Models.- References.- Subject Index.

Editorial Reviews

From the reviews of the first edition:"This book deals with applications for matrices for the study of distributions of statistics arising in multivariate statistical analysis. . The book is well-written and, for a serious student or researcher interested in applications of matrices to multivariate statistical analysis, I recommend this book strongly." (B. L. S. Prakasa Rao, Zentralblatt MATH, Vol. 1079, 2006)