Minimax Estimation of Proportions under Random Sample Size

Abstract

We study the problem of how to estimate the parameters of a multivariate hypergeometric distribution when the sample size n is assumed to be an ancillary statistic. The minimax estimator for squared error loss is given. This estimator differs from the well-known minimax estimator for fixed n. Furthermore, that classical estimator is shown to be not even admissible when n is random.

Key Words:

• Admissibility
• Ancillarity paradox
• Bayes estimator
• Multivariate hypergeometric distribution