Reducing sensitivity to nuisance parameters in semiparametric models: a quasi-score method

Abstract

This paper proposes a semiparametric extension of the projected score method of Waterman & Lindsay (1996) for the elimination of nuisance parameters. The procedure addresses cases where only the mean and the variance of the response variable are specified and where the mean function involves both parameters of interest and nuisance parameters. Important applications of the semiparametric model include quasilikelihood models for matched designs and for measurement error models (Carroll & Stefanski, 1990). As a result of the optimality and information-unbiasedness of the quasi-score function, a second-order quasi-score basis of estimating functions for the nuisance parameter is derived. Second-order locally ancillary estimating functions (Small & McLeish, 1994, pp. 81-4) are then obtained by solving a simple linear system that corresponds to a true projection for canonical exponential family distributions. Asymptotic arguments and simulation work show that the impact of nuisance parameters is considerably reduced when adopting the proposed approach.