AISM 52, 173-183

## 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.

**Source**
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