A nearly optimal two stage procedure

Abstract

This article is concerned with the problem of allocating a fixed number of trials between two independent normal populations with unknown means θ and ω, in order to estimate the product θω with squared error loss. Introducing independent normal priors on θ and ω a two stage procedure is introduced and shown to be asymptotically optimal. This problem arises, most obviously, in situations of deter-mining area based on measurements of length and width.

Keywords:

• Bayes risk
• martingales
• uniform integrability

AMS Subject Classifications:

• 62L05
• 62L10