Advanced Multivariate Statistics with Matrices

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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.