Empirical bayes methods in sequential estimation

Abstract

The problem of Bayes sequential point estimation when the prior is not completely known is considered. When auxiliary data are available, a general empirical Bayes approach to the problem is proposed. The empirical Bayes procedures are shown to be asymptotically non deficient in certain cases involving exponentially and normally distributed data, provided that the number of auxiliary observations becomes large as the cost per observation becomes small.

Keywords:

• Martingale
• submartingale
• uniform integrability
• deficiency
• asymptotically non-deficient