Consider the problem of estimating a mean vector in a p-variate normal distribution under two-stage sequential sampling schemes. The paper proposes a stopping rule motivated by the James-Stein shrinkage estimator, and shows that the stopping rule and the corresponding shrinkage estimator asymptotically dominate the usual two-stage procedure under a sequence of local alternatives for p≥3. Also the results of Monte Carlo simulation for average sample sizes and risks of estimators are stated.
