(Received May 9, 1988; revised December 11, 1989)
Abstract. Based on a sample of size n, we investigate a class of estimators of the mean theta 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 p > 3. Simple approximations 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 theta 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.
Key words and phrases: Shrinkage estimates, multivariate normal, loss.