Open Access
Translator Disclaimer
October 1999 Statistical estimation in varying coefficient models
Jianqing Fan, Wenyang Zhang
Ann. Statist. 27(5): 1491-1518 (October 1999). DOI: 10.1214/aos/1017939139


Varying coefficient models are a useful extension of classical linear models. They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age. The appeal of these models is that the coef .cient functions can easily be estimated via a simple local regression.This yields a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when different coefficient functions admit different degrees of smoothness. This drawback can be repaired by using our proposed two-step estimation procedure.The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies show that the gain by the two-step procedure can be quite substantial.The methodology is illustrated by an application to an environmental data set.


Download Citation

Jianqing Fan. Wenyang Zhang. "Statistical estimation in varying coefficient models." Ann. Statist. 27 (5) 1491 - 1518, October 1999.


Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0977.62039
MathSciNet: MR2001A:62046
Digital Object Identifier: 10.1214/aos/1017939139

Primary: 62G07
Secondary: 62J12

Keywords: local linear fit , mean-squared errors , Optimal rate of convergence , varying coefficient models

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 5 • October 1999
Back to Top