The fourth-root-n consistency and the efficiency of profile likelihood

Yuichi Hirose
Victoria University of Wellington

Profile likelihood is a popular method of estimation in the presence of nuisance parameter. Especially, it is useful for estimation in semi-parametric models, since the method reduces the infinite-dimensional estimation problem to a finite-dimensional one.In this presentation, we show the efficiency of a semi-parametric maximum likelihood estimator based on the profile likelihood. By introducing a new parameterization, we improve 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 dealt with the direct quadratic expansion of the profile likelihood rather than an approximate one.

Session 1a, Statistical Methodology: 11:10 — 11:30, Room 446

Presentation Program