A 2-STAGE SPLINE SMOOTHING METHOD FOR PARTIALLY LINEAR-MODELS

Rice (1986) 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 non-parametric 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. We also show that the same holds for the partial regression estimate proposed independently by Denby (1986) and Speckman (1988). Asymptotic normality results for the parametric component are also shown for both estimates. Furthermore, we associate these estimates with Wellner's (1986) efficient scores methods.