LEADER 04089nam 22004815 450 001 9910300113303321 005 20200707101239.0 010 $a3-030-02185-8 024 7 $a10.1007/978-3-030-02185-6 035 $a(CKB)4100000007177251 035 $a(MiAaPQ)EBC5606190 035 $a(DE-He213)978-3-030-02185-6 035 $a(PPN)232471258 035 $a(EXLCZ)994100000007177251 100 $a20181127d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aShrinkage Estimation /$fby Dominique Fourdrinier, William E. Strawderman, Martin T. Wells 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (333 pages) 225 1 $aSpringer Series in Statistics,$x0172-7397 311 $a3-030-02184-X 327 $aChapter 1. Decision Theory Preliminaries -- Chapter 2. Estimation of a normal mean vector I -- Chapter 3. Estimation of a normal mean vector II -- Chapter 4. Spherically symmetric distributions -- Chapter 5. Estimation of a mean vector for spherically symmetric distributions I: known scale -- Chapter 6. Estimation of a mean vector for spherically symmetric distributions II: with a residual -- Chapter 7. Restricted Parameter Spaces -- Chapter 8. Loss and Confidence Level Estimation.-. 330 $aThis book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions. Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book. Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions. Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports. Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein?s identity doesn?t hold; Stein?s lemma and Stokes? theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions. 410 0$aSpringer Series in Statistics,$x0172-7397 606 $aStatistics  606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aBayesian Inference$3https://scigraph.springernature.com/ontologies/product-market-codes/S18000 615 0$aStatistics . 615 14$aStatistical Theory and Methods. 615 24$aBayesian Inference. 676 $a519.544 700 $aFourdrinier$b Dominique$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767894 702 $aStrawderman$b William E$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWells$b Martin T$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300113303321 996 $aShrinkage Estimation$91910228 997 $aUNINA