Note on Estimating the Improvement in Stein-Type Estimators

摘要

In estimating the mean of a multivariate normal distribution under squared error loss, the maximum likelihood estimation may be uniformly improved upon. For a dominating estimator, how may we estimate the improvement. Results from Efron and Morris enable a unique unbiased estimator of the improvement for orthogonally invariant estimators. However, this estimator needn't be admissible. We develop, for the James-Stein estimator, alternative improvement estimators. (Author)