In this paper we consider an example where for each i,i = 1,2, ... , n, the observations Xij , j = 1, 2, ... , k are i.i.d . Binomial (ni, θ). Based on a theory developed by us earlier, we propose estimates of θ which are asymptotically efficient under the assumption that k ≥ 2, the ni 's come from a finite set { 1, 2, ... , q} and some mild regularity conditions on the sequence {ni} and θ hold. We present the results of a simulation whlch indicate, among other thlngs, the asymptotic lower bound to variance is lower than or approximately equal to simulated Variances and a simple moment estimate of θ does as well as the asymptotically efficient estimates.
