ON THE OPTIMALITY OF ESTIMATORS BASED ON P-SUFFICIENT STATISTICS

VASANT P. BHAPKAR*

Department of Statistics, College of Arts and Sciences, University of Kentucky, Lexington, KY 40506-0027, U.S.A.

(Received October 17, 1997; revised April 30, 1998)

Abstract. For estimation of functions involving only parameters of interest, in the presence of nuisance parameters, some optimality properties are established for partially sufficient (i.e. p-sufficient) statistics in two classes of regular probability models. The results are based on a characterization of regular unbiased estimating functions for parameters of interest in probability models for which a statistic exists such that its marginal distribution depends on unknown parameters only through the parameters of interest.

Key words and phrases: Fisher information, generalized Fisher information, partial sufficiency, ancillary statistic.