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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.

62J05 Linear regression; mixed models
62G07 Density estimation
62E20 Asymptotic distribution theory in statistics
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