The Annals of Statistics

Data-Driven Efficient Estimators for a Partially Linear Model

Hung Chen and Jyh-Jen Horng Shiau

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Chen and Shiau showed that a two-stage spline smoothing method and the partial regression method lead to efficient estimators for the parametric component of a partially linear model when the smoothing parameter is a deterministic sequence tending to zero at an appropriate rate. This paper is concerned with the large-sample behavior of these estimators when the smoothing parameter is chosen by the generalized cross validation (GCV) method or Mallows' $C_L$. Under mild conditions, the estimated parametric component is asymptotically normal with the usual parametric rate of convergence for both spline estimation methods. As a by-product, it is shown that the "optimal rate" for the smoothing parameter, with respect to expected average squared error, is the same for the two estimation methods as it is for ordinary smoothing splines.

Article information

Ann. Statist., Volume 22, Number 1 (1994), 211-237.

First available in Project Euclid: 11 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G05: Estimation
Secondary: 62G99: None of the above, but in this section 62J99: None of the above, but in this section

Partial splines semiparametric regression smoothing splines rate of convergence partial regression generalized cross validation Mallows' $C_L$ efficient estimators


Chen, Hung; Shiau, Jyh-Jen Horng. Data-Driven Efficient Estimators for a Partially Linear Model. Ann. Statist. 22 (1994), no. 1, 211--237. doi:10.1214/aos/1176325366.

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