Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 1, pp. 115--120

ON ESTIMATING SEVERAL BINOMIAL $N$'S

By

GEORGE CASELLA, *Cornell University*

and

WILLIAM E. STRAWDERMAN, *Rutgers University*

SUMMARY. We study the problem of estimating several binomial sample sizes under the assumption that the true proportions are known and equal. The loss function is taken to be the sum of squared errors divided by the true sample sizes. The improved estimators are similar in form to the Clevenson-Zidek estimators in the problem of estimating several Poisson parameters. We also study the problem of estimating the expected value of several binomials with equal but unknown proportion and unknown sample sizes. For this problem, we find an improved estimator if p is bounded above by some p_{0} < 1. If p is unrestricted, the usual estimator is shown to be admissible.

*AMS (1980) subject classification.* 62F10, 62C20.

*Key words and phrases.* Binomial distribution, estimation of sample size, admissibility.