In this paper, we outline a general approach to estimating the parametric component of a semiparametric model. For the case of a scalar parametric component, the method is based on the idea of first estimating a one-dimensional subproblem of the original problem that is least favorable in the sense of Stein. The likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem. The scalar parameter is then estimated by maximizing this "generalized profile likelihood." This method of estimation is applied to a particular class of semiparametric models, where it is shown that the resulting estimator is asymptotically efficient.
@article{1176348889,
author = {Severini, Thomas A. and Wong, Wing Hung},
title = {Profile Likelihood and Conditionally Parametric Models},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1768-1802},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348889}
}
Severini, Thomas A.; Wong, Wing Hung. Profile Likelihood and Conditionally Parametric Models. Ann. Statist., Tome 20 (1992) no. 1, pp. 1768-1802. http://gdmltest.u-ga.fr/item/1176348889/