Average worth estimation of the selected subset of Poisson populations

Let Π1, …, Π p be p(p≥2) independent Poisson populations with unknown parameters θ1, …, θ p , respectively. Let X i denote an observation from the population Π i , 1≤i≤p. Suppose a subset of random size, which includes the best population corresponding to the largest (smallest) θ i , is selected using Gupta and Huang [On subset selection procedures for Poisson populations and some applications to the multinomial selection problems, in Applied Statistics, R.P. Gupta, ed., North-Holland, Amsterdam, 1975, pp. 97–109] and (Gupta et al. [On subset selection procedures for Poisson populations, Bull. Malaysian Math. Soc. 2 (1979), pp. 89–110]) selection rule. In this paper, the problem of estimating the average worth of the selected subset is considered under the squared error loss function. The natural estimator is shown to be biased and the UMVUE is obtained using Robbins [The UV method of estimation, in Statistical Decision Theory and Related Topics-IV, S.S. Gupta and J.O. Berger, eds., Springer, New York, vo...