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＜電子ブック＞
Stein Estimation / by Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman
(JSS Research Series in Statistics. ISSN:23640065)

版	1st ed. 2023.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	VIII, 130 p. 3 illus : online resource
著者標目	*Maruyama, Yuzo author Kubokawa, Tatsuya author Strawderman, William E author SpringerLink (Online service)
件　名	LCSH:Statistics  FREE:Applied Statistics FREE:Statistical Theory and Methods FREE:Bayesian Inference FREE:Bayesian Network
一般注記	1. Decision Theory Preliminaries -- 2. Minimaxity and Improvement on the James-Stein estimator -- 3. Admissibility This book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book begins with a brief discussion of basic notions and results from decision theory such as admissibility, minimaxity, and (generalized) Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein estimator in the first chapter. In the following chapters, the authors consider estimation of the mean vector of a multivariate normal distribution in the known and unknown scale case when the covariance matrix is a multiple of the identity matrix and the loss is scaled squared error. The focus is on admissibility, inadmissibility, and minimaxity of (generalized) Bayes estimators, where particular attention is paid to the class of (generalized) Bayes estimators with respect to an extended Strawderman-type prior. For almost all results of this book, the authors present a self-contained proof. The book is helpful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics HTTP:URL=https://doi.org/10.1007/978-981-99-6077-4

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