## The Annals of Statistics

### Data-Driven Efficient Estimators for a Partially Linear Model

#### Abstract

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

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

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176325366

Digital Object Identifier
doi:10.1214/aos/1176325366

Mathematical Reviews number (MathSciNet)
MR1272081

Zentralblatt MATH identifier
0806.62029

JSTOR