The purpose of this chapter is to extend the M-estimation results of Chapter 14 to semiparametric M-estimation, where there is both a Euclidean parameter of interest Θ and a nuisance parameter η. Obviously, the semiparametric maximum likelihood estimators we have been discussing in the last several chapters are important examples of semiparametric M-estimators, where the objective function is an empirical likelihood. However, there are numerous other examples of semiparametric M-estimators, including estimators obtained from misspecified semiparametric likelihoods, least-squares, least-absolute deviation, and penalized maximum likelihood (which we discussed some in Sections 4.5 and 15.1 and elsewhere). In this chapter, we will try to provide general results on estimation and inference for semiparametric M-estimators, along with several illustrative examples. The material for this chapter is adapted from Ma and Kosorok (2005b).
KeywordsOrdinary Little Square Maximum Likelihood Estimator Outer Probability Asymptotic Normality Nuisance Parameter
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