Simultaneous estimation in the multiparameter gamma distribution under weighted quadratic losses (Q1081993)

A new class of solutions to a general differential inequality often encountered in multiparameter estimation problems is obtained. These solutions are used to form improved estimators for the scale parameters as well as the natural parameters of independent gamma distributions for a large class of weighted quadratic losses. The improved estimators permit exact analytical representation of the risk improvement. For the ordinary squared-error loss, a broader class of improved estimators is obtained; these improved estimators have an empirical Bayes interpretation. Numerical results are given which indicate the extent of risk improvement in certain situations.