On The Optimality of Estimators Based On P-Sufficient Statistics

Vasant P. Bhapkar

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.
AMS 1991 subject classification. Primary 62A20; secondary 62F11, 62B10.

Keywords: Fisher information, generalized Fisher information, partial sufficiency, regular unbiased estimating function, ancillary statistic.

Here is the full postscript text for this technical report. It is 185354 bytes long.