Open Access
June 2012 Flexible generalized varying coefficient regression models
Young K. Lee, Enno Mammen, Byeong U. Park
Ann. Statist. 40(3): 1906-1933 (June 2012). DOI: 10.1214/12-AOS1026


This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition we give a general theorem that the problem of estimating the multivariate mean function is equivalent to that of estimating its univariate component functions. We discuss implications of the theorem for sieve and penalized least squares estimators, and then investigate the outcomes in full details for a kernel-type estimator. The kernel estimator is given as a solution of a system of nonlinear integral equations. We provide an iterative algorithm to solve the system of equations and discuss the theoretical properties of the estimator and the algorithm. Finally, we give simulation results.


Download Citation

Young K. Lee. Enno Mammen. Byeong U. Park. "Flexible generalized varying coefficient regression models." Ann. Statist. 40 (3) 1906 - 1933, June 2012.


Published: June 2012
First available in Project Euclid: 16 October 2012

zbMATH: 1257.62040
MathSciNet: MR3015048
Digital Object Identifier: 10.1214/12-AOS1026

Primary: 62G08
Secondary: 62G20

Keywords: Entropy , Hilbert space , integral equation , kernel smoothing , Newton–Raphson approximation , projection , quasi-likelihood , varying coefficient models

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
Back to Top