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Stein Estimation

  • Book
  • © 2023

Overview

Authors:
  1. Yuzo Maruyama

    1. Grad. School of Business Administration, Kobe University, Kobe-shi, Japan

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  2. Tatsuya Kubokawa

    1. Faculty of Economics, University of Tokyo, Tokyo, Japan

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  3. William E. Strawderman

    1. Department of Statistics, Rutgers University, Piscataway, USA

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  • Integrates modern and classical shrinkage estimation and contributes to further developments in the field
  • Presents direct proof of Brown’s 1971 seminal work on determination of admissibility of generalized Bayes estimators
  • Presents recent results of admissibility of generalized Bayes estimators in the presence of a nuisance scale parameter

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

Part of the book sub series: JSS Research Series in Statistics (JSSRES)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-viii
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  2. The Stein Phenomenon

    • Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman
    Pages 1-22

  3. Estimation of a Normal Mean Vector Under Known Scale

    • Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman
    Pages 23-43

  4. Estimation of a Normal Mean Vector Under Unknown Scale

    • Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman
    Pages 45-76

  5. Back Matter

    Pages 77-130
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Keywords

About this book

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.


Authors and Affiliations

  • Grad. School of Business Administration, Kobe University, Kobe-shi, Japan

    Yuzo Maruyama

  • Faculty of Economics, University of Tokyo, Tokyo, Japan

    Tatsuya Kubokawa

  • Department of Statistics, Rutgers University, Piscataway, USA

    William E. Strawderman

About the authors

Yuzo Maruyama is Professor of Statistics at Kobe University. He earned his M.S. and Ph.D. degrees, both in Economics, at the University of Tokyo. His research interests include statistical decision theory, shrinkage estimation, and Bayesian model selection.


Tatsuya Kubokawa is Professor in the Faculty of Economics at the University of Tokyo. He earned his M.S. and Ph.D. degrees, both in Mathematics, at University of Tsukuba. His research interests include statistical decision theory, multivariate analysis, and mixed-effects modeling.


William E. Strawderman is Professor of Statistics at Rutgers University. He earned an M.S. in Mathematics from Cornell University and a second M.S. in Statistics from Rutgers and then completed his Ph.D. in Statistics, also at Rutgers. He is Fellow of both the Institute of Mathematical Statistics and American Statistical Society and Elected Member at International Statistical Institute. His research interests include statistical decision theory, shrinkage estimation, and Bayesian statistics.


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