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March, 1994 Data-Driven Efficient Estimators for a Partially Linear Model
Hung Chen, Jyh-Jen Horng Shiau
Ann. Statist. 22(1): 211-237 (March, 1994). DOI: 10.1214/aos/1176325366


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.


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Hung Chen. Jyh-Jen Horng Shiau. "Data-Driven Efficient Estimators for a Partially Linear Model." Ann. Statist. 22 (1) 211 - 237, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0806.62029
MathSciNet: MR1272081
Digital Object Identifier: 10.1214/aos/1176325366

Primary: 62G05
Secondary: 62G99, 62J99

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
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