Average worth and simultaneous estimation of the selected subset

Suppose a subset of populations is selected from the given k gamma G( _i,p ) (i = 1,2,...,k)populations, using Gupta's rule (1963, Ann. Inst. Statist. Math., 14, 199–216). The problem of estimating the average worth of the selected subset is first considered. The natural estimator is shown to be positively biased and the UMVUE is obtained using Robbins' UV method of estimation (1988, Statistical Decision Theory and Related Topics IV, Vol. 1 (eds. S. S. Gupta and J. O. Berger), 265–270, Springer, New York). A class of estimators that dominate the natural estimator for an arbitrary k is derived. Similar results are observed for the simultaneous estimation of the selected subset.