Annals of Statistics

Flexible generalized varying coefficient regression models

Young K. Lee, Enno Mammen, and Byeong U. Park

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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.

Article information

Source
Ann. Statist., Volume 40, Number 3 (2012), 1906-1933.

Dates
First available in Project Euclid: 16 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1350394521

Digital Object Identifier
doi:10.1214/12-AOS1026

Mathematical Reviews number (MathSciNet)
MR3015048

Zentralblatt MATH identifier
1257.62040

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Varying coefficient models kernel smoothing entropy projection Hilbert space quasi-likelihood integral equation Newton–Raphson approximation

Citation

Lee, Young K.; Mammen, Enno; Park, Byeong U. Flexible generalized varying coefficient regression models. Ann. Statist. 40 (2012), no. 3, 1906--1933. doi:10.1214/12-AOS1026. https://projecteuclid.org/euclid.aos/1350394521


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