Combining Possibly Related Estimation Problems

Abstract

Summary We have two sets of parameters we wish to estimate, and wonder whether the James-Stein estimator should be applied separately to the two sets or once to the combined problem. We show that there is a class of compromise estimators, Bayesian in nature, which will usually be preferred to either alternative. “The difficulty here is to know what problems are to be combined together— why should not all our estimation problems be lumped together into one grand melée?” George Barnard commenting on the James–Stein estimator, 1962.