Convergence Rate of K-Step Maximum Likelihood Estimate in Semiparametric Models

摘要

We suggest an iterative approach to computing K-step maximum likelihoodestimates (MLE) of the parametric components in semiparametric models based ontheir profile likelihoods. The higher order convergence rate of K-step MLEmainly depends on the precision of its initial estimate and the convergencerate of the nuisance functional parameter in the semiparametric model.Moreover, we can show that the K-step MLE is as asymptotically efficient as theregular MLE after a finite number of iterative steps. Our theory is verifiedfor several specific semiparametric models. Simulation studies are alsopresented to support these theoretical results.