Let π1, π2, . . . , πk be k independent populations, where πi ∼ G(θi, pi), the gamma distribution with θi as the unknown scale parameter, and pi as the known shape parameter. Let {X1, . . . , Xk} be a random sample, where Xi is from πi. Suppose a subset of the above populations is selected using Gupta's subset selection procedure, according to which πi is selected iff Xi ≥ cX[1], where X[1] = max {X1, . . ., Xk}, and c is a suitable constant. In this paper, we obtain the empirical Bayes estimators for the means of the selected populations. For the squared error loss, it is shown that the empirical Bayes estimators are inadmissible and the dominating estimators are also obtained, using the technique of solving differential inequalities.
