EAN: 9784431553861

SPRINGERBRIEFS IN STATISTICS APPLIED MATRIX A...

This book provides comprehensive reviews of recent progress in matrix variate and tensor
variate data analysis from applied points of view. Matrix and tensor approaches for data
analysis are known to be extremely useful for recently emerging complex and high-dimensional
data in various applied fields. The reviews contained herein cover recent applications of these
methods in psychology (Chap. 1)  audio signals (Chap. 2)   image analysis from tensor principal
component analysis (Chap. 3)  and image analysis from decomposition (Chap. 4)  and genetic data
(Chap. 5) . Readers will be able to understand the present status of these techniques as
applicable to their own fields. In Chapter 5 especially  a theory of tensor normal
distributions  which is a basic in statistical inference  is developed  and multi-way
regression  classification  clustering  and principal component analysis are exemplified under
tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate and tensor
variate normal distributions  whose theory under multivariate normal distributions has been a
popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al.
(1988). Chapters 1  5  and 6 distinguish this book from ordinary engineering books on these
topics.

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