  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.
