Estimating Equations with Nuisance Parameters: Theory and Applications

Abstract

In a variety of statistical problems the estimate Θn of a parameter Θ is defined as the root of a generalized estimating equation Gn(Θnγn)=0 where γn is an estimate of a nuisance parameter γ. We give sufficient conditions for the asymptotic normality of #x0398;n defined in this way and derive their asymptotic distribution. A circumstance under which the asymptotic distribution of #x0398;n will not be influenced by that of γn) is noted. As an example, we consider a covariance structure analysis in which both the population mean and the population fourth-order moment are nuisance parameters. Applications to pseudo maximum likelihood, generalized least squares with estimated weights, and M-estimation with an estimated scale parameter are discussed briefly.