Estimating Functions, Partial Sufficiency and Q-Sufficiency in the Presence of Nuisance Parameters

Vasant P. Bhapkar

Abstract:

When there exists a statistic which has its distribution free of nuisance parameters, the optimality of the marginal score function can be investigated in the context of generalized Fisher information for parameters of interest. In the case of a partially sufficient statistic, i.e. a statistic sufficient for parameters of interest, the marginal score function is the optimal estimating function. With the new concept of q-sufficiency for parameters of interest, the marginal score function is operationally equivalent to the optimal estimating function.
AMS Subject Classification: 62A20, 62F99

Key Words: Generalized Fisher information matrix, completeness of a family, partial sufficiency.

Here is the full postscript text for this technical report. It is 251659 bytes long.