A class of multiple shrinkage estimators

Based on a sample of size n, we investigate a class of estimators of the mean of a p-variate normal distribution with independent components having unknown covariance. This class includes the James-Stein estimator and Lindley's estimator as special cases and was proposed by Stein. The mean squares error improves on that of the sample mean for p3. Simple approximations imations for this improvement are given for large n or p. Lindley's estimator improves on that of James and Stein if either n is large, and the coefficient of variation of is less than a certain increasing function of p, or if p is large. An adaptive estimator is given which for large samples always performs at least as well as these two estimators.