Shrinkage estimation
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.
scientific article; zbMATH DE number 6967914