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＜電子ブック＞
Shrinkage Estimation for Mean and Covariance Matrices / by Hisayuki Tsukuma, Tatsuya Kubokawa
(JSS Research Series in Statistics. ISSN:23640065)

版	1st ed. 2020.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	IX, 112 p. 1 illus : online resource
著者標目	*Tsukuma, Hisayuki author Kubokawa, Tatsuya author SpringerLink (Online service)
件　名	LCSH:Biometry LCSH:Statistics  FREE:Biostatistics FREE:Statistical Theory and Methods
一般注記	Preface -- Decision-theoretic approach to estimation -- Matrix theory -- Matrix-variate distributions -- Multivariate linear model and invariance -- Identities for evaluating risk -- Estimation of mean matrix -- Estimation of covariance matrix -- Index This book provides a self-contained introduction to shrinkage estimation for matrix-variate normal distribution models. More specifically, it presents recent techniques and results in estimation of mean and covariance matrices with a high-dimensional setting that implies singularity of the sample covariance matrix. Such high-dimensional models can be analyzed by using the same arguments as for low-dimensional models, thus yielding a unified approach to both high- and low-dimensional shrinkage estimations. The unified shrinkage approach not only integrates modern and classical shrinkage estimation, but is also required for further development of the field. Beginning with the notion of decision-theoretic estimation, this book explains matrix theory, group invariance, and other mathematical tools for finding better estimators. It also includes examples of shrinkage estimators for improving standard estimators, such as least squares, maximum likelihood, and minimum risk invariant estimators, and discusses the historical background and related topics in decision-theoretic estimation of parameter matrices. This book is useful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics HTTP:URL=https://doi.org/10.1007/978-981-15-1596-5

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