The Annals of Statistics

Statistical estimation in varying coefficient models

Jianqing Fan and Wenyang Zhang

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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.

Article information

Ann. Statist., Volume 27, Number 5 (1999), 1491-1518.

First available in Project Euclid: 23 September 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62J12: Generalized linear models

Varying coefficient models local linear fit optimal rate of convergence mean-squared errors


Fan, Jianqing; Zhang, Wenyang. Statistical estimation in varying coefficient models. Ann. Statist. 27 (1999), no. 5, 1491--1518. doi:10.1214/aos/1017939139.

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