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.

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