A two-stage spline smoothing method for partially linear models. (English) Zbl 0741.62039
J. Rice [Stat. Probab. Lett. 4, 203-208 (1986; Zbl 0628.62077)] showed that the partial spline estimate of the parametric component in a semiparametric regression model is generally biased and it is necessary to undersmooth the nonparametric component to force the bias to be negligible with respect to the standard error. We propose a two-stage spline smoothing method for estimating the parametric and nonparametric components in a semiparametric model. By appropriately choosing rates for smoothing parameters, we show that the parametric component can be estimated at the parametric rate with the new estimate without undersmoothing the nonparametric component.
Keywords:
rate of convergence; partial regression; efficient scores; additive models; partial spline estimate; parametric component; semiparametric regression; bias; two-stage spline smoothing method; nonparametric components; smoothing parametersCitations:
Zbl 0628.62077References:
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