IMPROVED ESTIMATORS OF THE NATURAL PARAMETERS IN CONTINUOUS MULTIPARAMETER EXPONENTIAL FAMILIES
ABSTRACT In this paper we first present general solutions to a differential inequality. These results include some of those of Berger, Ghosh and Parsian, and Ghosh, Hwang and Tsui[1], 6-7 as special cases. We then apply these results to the problem of estimating the natural parameter vector under a quadratic loss in continuous multiparameter exponential families. Also, we construct some classes of estimators dominating (linear functions of) the uniformly minimum variance unbiased estimator (UMVUE) or an estimator which is a known constant multiple of the UMVUE in cases of sampling from normal, gamma and generalized gamma distributions. Finally, in the case of sampling from normal distribution, we compare dominating estimators in each class with themselves in some special cases and demonstrate where our method can be failed in the case when the initial estimator is known to be admissible.