# Second Order Approximation in the Partially Linear Regression Model

Oliver Linton
Econometrica
Vol. 63, No. 5 (Sep., 1995), pp. 1079-1112
DOI: 10.2307/2171722
Stable URL: http://www.jstor.org/stable/2171722
Page Count: 34

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## 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 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.

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