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

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

2007-08-22

arxiv.org/abs/0708.3041v1

Mathematics

Statistics Theory

22 pages, 2 tables

Scientific paper

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.

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