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Shrinkage Estimation

  • Dominique Fourdrinier
  • William E. Strawderman
  • Martin T. Wells

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 1-28
  3. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 29-61
  4. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 63-126
  5. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 127-150
  6. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 151-177
  7. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 179-213
  8. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 215-235
  9. Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
    Pages 237-276
  10. Back Matter
    Pages 277-333

About this book

Introduction

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.

Keywords

Minimax Estimation Bayes Estimation Shrinkage Estimation Multivariate Statistics Spherical Symmetry Decision Theory Mathematical Statistics

Authors and affiliations

  • Dominique Fourdrinier
    • 1
  • William E. Strawderman
    • 2
  • Martin T. Wells
    • 3
  1. 1.Mathématiques, BP 12Université de RouenSt-Étienne-du-RouvrayFrance
  2. 2.Department of StatisticsRutgers UniversityPiscatawayUSA
  3. 3.Department of Statistical ScienceCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02185-6
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02184-9
  • Online ISBN 978-3-030-02185-6
  • Series Print ISSN 0172-7397
  • Series Online ISSN 2197-568X
  • Buy this book on publisher's site
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