Stein estimation

Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman (Autoren)

Buch | Softcover

130 Seiten

2023 | 1. Auflage
Springer (Verlag)
978-981-99-6076-7 (ISBN)

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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.

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.

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

Erscheinungsdatum	04.10.2023
Reihe/Serie	JSS Research Series in Statistics
Zusatzinfo	Illustrationen
Verlagsort	Singapur
Sprache	englisch
Maße	155 x 235 mm
Gewicht	225 g
Einbandart	kartoniert
Themenwelt	Mathematik / Informatik ► Mathematik ► Statistik
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	admissibility • Bayes • James-Stein Estimator • minimaxity • Stein Paradox
ISBN-10	981-99-6076-2 / 9819960762
ISBN-13	978-981-99-6076-7 / 9789819960767
Zustand	Neuware