# Econometrica

## Journal Of The Econometric Society

### An International Society for the Advancement of Economic Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 1995, Volume 63, Issue 5

# Second Order Approximation in the Partially Linear Regression Model

Oliver Linton

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.