Stein Estimation

1. Auflage 2023
ISBN: 978-981-99-6076-7
Verlag: Springer Nature Singapore

Buch, Englisch, 130 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 224 g

Reihe: SpringerBriefs in Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Maruyama, Yuzo

Strawderman, William E.

Kubokawa, Tatsuya

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz

Inhaltsverzeichnis

1. Decision Theory Preliminaries.- 2. Minimaxity and Improvement on the James-Stein estimator.- 3. Admissibility.

Über Autor(innen)

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.