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

TL;DR

This paper introduces an iterative method for computing K-step MLEs in semiparametric models, demonstrating finite-step efficiency and convergence properties through theoretical analysis and simulations.

Contribution

It provides a new iterative approach for K-step MLEs in semiparametric models, establishing their convergence rate and asymptotic efficiency after finite steps.

Findings

K-step MLE converges at a higher rate depending on initial estimate and nuisance parameter convergence.

K-step MLE achieves asymptotic efficiency after finite iterations.

Simulation results support the theoretical convergence and efficiency claims.

Abstract

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