ASYMPTOTIC COMPARISONS OF U-STATISTICS, V-STATISTICS AND LIMITS OF BAYES ESTIMATES BY DEFICIENCIES

Abstract

As estimators of estimable parameters, we consider three statistics which are U-statistic, V-statistic and limit of Bayes estimate. This limit of Bayes estimate, called LB-statistic in this paper, is obtained from Bayes estimate of estimable parameter based on Dirichlet process, by letting its parameter tend to zero. For the estimable parameter with non-degenerate kernel, the asymptotic relative efficiencies of LB-statistic with respect to U-statistic and V-statistic and that of V-statistic with respect to U-statistic are equal to one. We show asymptotic differences among LB-statistic, U-statistic and V-statistic by using the deficiency.