**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 1, pp. 160--170

**ON A CLASS OF SEQUENTIAL ESTIMATION PROBLEMS FOR ONE-PARAMETER EXPONENTIAL FAMILIES**

By

RYSZARD MAGIERA, *Technical University of Wroclaw*

SUMMARY. The problem of estimating the mean value parameter of a one parameter exponential family of distributions is considered in the case when data is forthcoming only at random times. Using a weighted square error loss related to the Fisher information, and the observation cost determined by a function of moment of stopping, a class of optimal sequential procedures is derived.

*AMS (1991) subject classification.* Primary 62L12, 62L15, secondary 62C10.

*Key words and phrases.* Bayes sequential estimation, sequential decision procedure, stopping time, exponential family of distributions, conjugate priors.