In a partial linear model, the dependence of a response variate Y on covariates (W, X$ is given by $$Y = W \beta + \eta(X) + \mathscr{E}$$ where $\mathscr{E}$ is independent of $(W, X)$ with densities g and f, respectively. In this paper an asymptotically efficient estimator of $\beta$ is constructed solely under mild smoothness assumptions on the unknown $\eta$, f and g, thereby removing the assumption of finite residual variance on which all least-squares-type estimators available in the literature are based.
@article{1034276628,
author = {Bhattacharya, P. K. and Zhao, Peng-Liang},
title = {Semiparametric inference in a partial linear model},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 244-262},
language = {en},
url = {http://dml.mathdoc.fr/item/1034276628}
}
Bhattacharya, P. K.; Zhao, Peng-Liang. Semiparametric inference in a partial linear model. Ann. Statist., Tome 25 (1997) no. 6, pp. 244-262. http://gdmltest.u-ga.fr/item/1034276628/