Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution,
RAND CORP SANTA MONICA CALIF
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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.
- Statistics and Probability