03057nam 22006255 450 991099394450332120250316135535.09789819960774981996077010.1007/978-981-99-6077-4(MiAaPQ)EBC30761277(Au-PeEL)EBL30761277(DE-He213)978-981-99-6077-4(CKB)28349519500041(EXLCZ)992834951950004120230929d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStein Estimation /by Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman1st ed. 2023.Singapore :Springer Nature Singapore :Imprint: Springer,2023.1 online resource (0 pages)JSS Research Series in Statistics,2364-00659789819960767 9819960762 Includes bibliographical references.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.JSS Research Series in Statistics,2364-0065StatisticsStatisticsApplied StatisticsStatistical Theory and MethodsBayesian InferenceBayesian NetworkStatistics.Statistics.Applied Statistics.Statistical Theory and Methods.Bayesian Inference.Bayesian Network.519.544Maruyama Yuzo1745419Kubokawa TatsuyaStrawderman William E.MiAaPQMiAaPQMiAaPQBOOK9910993944503321Stein Estimation4369860UNINA