We examine the second order properties of various quantities of interest in the partially linear regression model. We obtain a stochastic expansion with remainder oP(n -2µ), where µ < 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.
Semiparametric estimation, Partially linear regression, Kernel, Local polynomial, Second order approximations, Bandwidth choice, Asymptotic expansions