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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

Abstract

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.

Citation

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

Information

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

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

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • June 2012
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