
Accession Number : AD0786587
Title : Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Efron,Bradley ; Morris,Carl
Report Date : MAR 1974
Pagination or Media Count : 25
Abstract : Ever since Charles Stein proved that for squared error loss the sample mean X of a multivariate normal distribution is an inadmissible estimator of its expectation theta, statisticians have searched for uniformly better (minimax) estimators with good properties. Stein has found an unbiased estimator for the risk function of an arbitrary estimator of theta, when the dispersion matrix sigma of X is known. The authors extend this very useful result to include unbiased estimates of the risk function in two cases where sigma must be estimated. This formula is used in the main theorem, to obtain more general conditions than previously published. Finally it is proven that the limited translation estimators, which are not orthogonally invariant, of Efron and Morris are minimax.
Descriptors : *Multivariate analysis, *Risk, Normal density functions, Minimax technique, Estimates, Theorems
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE