COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1065

Second Order Approximation in the Partially Linear Regression Model

Oliver Linton

December 1993

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.

Keywords: Semiparametric estimation, Partially linear regression, Kernel, Local polynomial, Second order approximations, Bandwidth choice, Asymptotic expansions