Running Head: EFFICIENCY OF PROFILE LIKELIHOOD EFFICIENCY OF PROFILE LIKELIHOOD IN SEMI-PARAMETRIC MODELS

Profile likelihood is a popular method of estimation in the presence of a nuisance parameter. It is especially useful for estimation in semi-parametric models, since the method reduces the infinite-dimensional estimation problem to a finite-dimensional one. In this paper we investigate the efficiency of a semi-parametric maximum likelihood estimator based on the profile likelihood. By introducing a new parameterization, we improve on the seminal work of Murphy and van der Vaart (2000) in two ways: we prove the no bias condition in a general semi-parametric model context, and deal with the direct quadratic expansion of the profile likelihood rather than an approximate one. To illustrate the method, an application to two-phase, outcome-dependent sampling design is given