BAYES SEQUENTIAL ESTIMATION OF POISSON MEAN UNDER A LINEX LOSS FUNCTION

Abstract

This paper considers Bayes sequential estimation of the mean of a Poisson distribution using a LINEX loss function and a cost c > 0 for each observation. Under a Gamma prior distribution, it is shown that an asymptotically pointwise optimal rule is asymptotically non-deficient in the sense of Woodroofe (1981).

Keywords:

• LINEX loss function
• Bayes sequential estimation
• A.P.O. rule
• Poisson distribution
• Non-deficiency

ACKNOWLEDGMENTS

The author wishes to thank an associate editor and a referee for their helpful comments.