Stein Estimation / by Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman.

Format:

Book

Author/Creator:

Maruyama, Yuzo, author.

Kubokawa, Tatsuya, author.

Strawderman, William E., author.

Series:

JSS Research Series in Statistics, 2364-0065

Language:

English

Subjects (All):

Statistics.

Applied Statistics.

Statistical Theory and Methods.

Bayesian Inference.

Bayesian Network.

Local Subjects:

Applied Statistics.

Statistical Theory and Methods.

Bayesian Inference.

Bayesian Network.

Physical Description:

1 online resource (0 pages)

Edition:

1st ed. 2023.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2023.

Summary:

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.

Contents:

1. Decision Theory Preliminaries

2. Minimaxity and Improvement on the James-Stein estimator

3. Admissibility.

Notes:

Includes bibliographical references.

ISBN:

9789819960774

9819960770