Sufficiency and Rao-Blackwell Theorem in the Presence of Nuisance Parameters

Vasant P. Bhapkar

Abstract:

In the class of regular distributions sufficiency with respect to the parameters of interest (i.e. p-sufficiency), in the presence of unknown nuisance parameters, is defined in the sense that the p-sufficient statistic contains all the generalized Fisher information. Optimality properties of such p-sufficient statistics are described in the context of estimating functions for parameters of interest, and also for estimation of parametric functions.

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