LEADER 03057nam 22006255 450 001 9910993944503321 005 20250316135535.0 010 $a9789819960774 010 $a9819960770 024 7 $a10.1007/978-981-99-6077-4 035 $a(MiAaPQ)EBC30761277 035 $a(Au-PeEL)EBL30761277 035 $a(DE-He213)978-981-99-6077-4 035 $a(CKB)28349519500041 035 $a(EXLCZ)9928349519500041 100 $a20230929d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStein Estimation /$fby Yuzo Maruyama, Tatsuya Kubokawa, William E. Strawderman 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (0 pages) 225 1 $aJSS Research Series in Statistics,$x2364-0065 311 08$a9789819960767 311 08$a9819960762 320 $aIncludes bibliographical references. 327 $a1. Decision Theory Preliminaries -- 2. Minimaxity and Improvement on the James-Stein estimator -- 3. Admissibility. 330 $aThis book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book begins with a brief discussion of basic notions and results from decision theory such as admissibility, minimaxity, and (generalized) Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein estimator in the first chapter. In the following chapters, the authors consider estimation of the mean vector of a multivariate normal distribution in the known and unknown scale case when the covariance matrix is a multiple of the identity matrix and the loss is scaled squared error. The focus is on admissibility, inadmissibility, and minimaxity of (generalized) Bayes estimators, where particular attention is paid to the class of (generalized) Bayes estimators with respect to an extended Strawderman-type prior. For almost all results of this book, the authors present a self-contained proof. The book is helpful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics. 410 0$aJSS Research Series in Statistics,$x2364-0065 606 $aStatistics 606 $aStatistics 606 $aApplied Statistics 606 $aStatistical Theory and Methods 606 $aBayesian Inference 606 $aBayesian Network 615 0$aStatistics. 615 0$aStatistics. 615 14$aApplied Statistics. 615 24$aStatistical Theory and Methods. 615 24$aBayesian Inference. 615 24$aBayesian Network. 676 $a519.544 700 $aMaruyama$b Yuzo$01745419 702 $aKubokawa$b Tatsuya 702 $aStrawderman$b William E. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910993944503321 996 $aStein Estimation$94369860 997 $aUNINA