The asymptotically pointwise optimal testing rule and its competitors – an empirical bayes approach

Abstract

In this paper,the performance of asymptotically pointwise optimal procedures is studied for fixed c, the cost per unit sample. Our treatment is focused on a statistical hypothesis testing problem, namely,the linear loss two-action problem. Using the empirical Bayes approach, we construct a sequential testing procedure which dominates the A.P.O. testing procedure when the number of auxiliary data available is large. It is shown that this domination occurs for most natural cases of the A.P.O. stopping rule. The comparison of the two procedures is made by comparing their respective Bayes risks.

Keywords:

• Asymptotically Pointwise Optimal
• Empriical Bayes
• Linear loss two-action problem