Shrinkage Estimation. 1st ed. 2018

種類:

電子ブック

責任表示:

by Dominique Fourdrinier, William E. Strawderman, Martin T. Wells

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Fourdrinier, Dominique.
• Strawderman, William E.
• Wells, Martin T.
• SpringerLink (Online service)

シリーズ名:

Springer Series in Statistics ;

ISBN:

9783030021856 [3030021858]    

注記:

Chapter 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.-.
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

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