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Title Shrinkage estimation / Dominique Fourdrinier, William E. Strawderman, Martin T. Wells.
Imprint Cham, Switzerland : Springer, [2018]

View online
View online
Series Springer series in statistics.
Springer series in statistics.
Subject Estimation theory.
Alt Name Fourdrinier, Dominique, 1951-
Strawderman, William E.,
Wells, Martin (Martin T.),
Description 1 online resource.
polychrome rdacc
Note Includes index.
Contents Decision theory preliminaries -- Estimation of normal mean vector I -- Estimation of normal mean vector II -- Spherically symmetric distributions -- Estimation of a mean vector for spherically symmetric distribtuions I : known scale -- Estimation of a mean vector for spherically symmetric distributions II : with a residual -- Restricted parameter spaces -- Loss and confidence level estimation.
Summary This 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.
Note Online resource; title from PDF title page (EBSCO, viewed November 30, 2018).
ISBN 9783030021856 (electronic bk.)
3030021858 (electronic bk.)
ISBN/ISSN 10.1007/978-3-030-02185-6
OCLC # 1076543376

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