Shrinkage estimation
type: Item
instance of: scholarly article
title: Shrinkage estimation
zbMATH Open document ID: 1411.62011
DOI: 10.1007/978-3-030-02185-6
author: Dominique Fourdrinier
author: William E. Strawderman
author: Martin T. Wells
published in: Springer Series in Statistics
publication date: 2018-10-29T00:00:00Z
review text: In shrinkage estimation certain basic estimators are improved by using additional information, available models, etc. Corresponding tools for updating initial estimators are Bayesian estimation methods, decision theoretical procedures.with corresponding loss functions, minimax procedures, extreme values of samples, invariance concepts, etc. After the presentation of some basics from stochastics and decision theory, methods of the above mentioned type are applied to the estimation of the mean/location vector of normal, spherically symmetric, elliptical symmetric distributions. Examples of shrinkage estimators are Bayesian estimators, having implicit shrinking properties, James-Stein estimator for the mean of Gaussian random vectors -- dominating the least square estimator --, and Baranchik estimators. Several examples and many references are given. The well-written volume, presenting the actual knowledge in this field, is suitable for readers having good background in analysis, linear algebra, probability theory and mathematical statistics.
reviewed by: Kurt Marti
Mathematics Subject Classification ID: 62-02
zbMATH DE Number: 6967914
zbMATH Keywords: shrinkage estimation
zbMATH Keywords: Bayesian estimators
zbMATH Keywords: minimum loss estimators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-02185-6
OpenAlex ID: W4247941414
description: scientific article; zbMATH DE number 6967914