Fixed-sample optimal non-orthogonal estimating functions in the presence of nuisance parameters

Abstract

In the paper, an important necessary and sufficient condition for a commonly used non-orthogonal estimating function to be fixed-sample optimal is proposed. The class of all fixed-sample optimal non-orthogonal estimating functions is characterized under the proposed condition. A simple counterexample without any fixed-sample optimal non-orthogonal estimating function is constructed to show that the proposed condition does not necessarily hold. The usefulness and applicability of the proposed method are illustrated by two classical examples with many nuisance parameters.