Conditional score functions: Some optimality results

The conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters (Godambe, 1976). The present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest. In this case, globally optimal estimating functions are impossible. A weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality.