Semiparametric inference in a partial linear model

Abstract

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.