p.1079

Second Order Approximation in the Partially Linear Regression Model

Oliver Linton

Abstract

We examine the second order properties of various quantities of interest in the partially linear regression model. We obtain a stochastic expansion with remainder $O_P(n^{-2\mu})$, where $\mu < 1/2$, for the standardized semiparametric least squares estimator, a standard error estimator, and a studentized statistic. We use the second order expansions to correct the standard error estimates for second order effects, and to define a method of bandwidth choice. A Monte Carlo experiment provides favorable evidence on our method of bandwidth choice.