# zbMATH — the first resource for mathematics

Second order approximation in the partially linear regression model. (English) Zbl 0836.62050
Summary: We examine the second order properties of various quantities of interest in the partially linear regession 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.

##### MSC:
 62J05 Linear regression; mixed models 62G07 Density estimation 62E20 Asymptotic distribution theory in statistics
Full Text: