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Titlebook: Shrinkage Estimation; Dominique Fourdrinier,William E. Strawderman,Marti Book 2018 Springer Nature Switzerland AG 2018 Minimax Estimation.

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书目名称Shrinkage Estimation
编辑Dominique Fourdrinier,William E. Strawderman,Marti
视频video
概述First book to explore Shrinkage Estimation as a global phenomenon.Focuses on point and loss estimation in multivariate normal and spherically symmetric distributions.Authors are at the forefront of Sh
丛书名称Springer Series in Statistics
图书封面Titlebook: Shrinkage Estimation;  Dominique Fourdrinier,William E. Strawderman,Marti Book 2018 Springer Nature Switzerland AG 2018 Minimax Estimation.
描述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
出版日期Book 2018
关键词Minimax Estimation; Bayes Estimation; Shrinkage Estimation; Multivariate Statistics; Spherical Symmetry;
版次1
doihttps://doi.org/10.1007/978-3-030-02185-6
isbn_ebook978-3-030-02185-6Series ISSN 0172-7397 Series E-ISSN 2197-568X
issn_series 0172-7397
copyrightSpringer Nature Switzerland AG 2018
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Decision Theory Preliminaries, sufficiency, completeness and unbiasedness at the level of, for example, Casella and Berger (.), Shao (.), or Bickel and Doksum (.). In the following, we will discuss, often without proof, some results in Bayesian decision theory, minimaxity, admissibility, invariance, and general linear models.
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Estimation of a Normal Mean Vector I,r will be concerned with the case of a known covariance matrix of the form . = .... and “usual quadratic loss,” .(., .) = ∥. − .∥. = (. − .).(. − .). Generalizations to known general covariance matrix ., and to general quadratic loss, .(., .) = (. − .)..(. − .), where . is a . × . symmetric non-nega
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Spherically Symmetric Distributions,tion vector could be improved upon quite generally for . ≥ 3 and Brown (.) substantially extended this conclusion to essentially arbitrary loss functions. Explicit results of the James-Stein type, however, have thus far been restricted to the case of the normal distribution. Recall the geometrical i
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