FLEXIBLE GENERALIZED VARYING COEFFICIENT REGRESSION MODELS

被引：45

作者：

Lee, Young K. ^{[1
]}

Mammen, Enno ^{[2
]}

Park, Byeong U. ^{[3
]}

机构：

[1] Kangwon Natl Univ, Dept Stat, Chunchon 200701, South Korea

[2] Univ Mannheim, Dept Econ, D-68131 Mannheim, Germany

[3] Seoul Natl Univ, Dept Stat, Seoul 151747, South Korea

来源：

ANNALS OF STATISTICS | 2012年 / 40卷 / 03期

关键词：

Varying coefficient models; kernel smoothing; entropy; projection; Hilbert space; quasi-likelihood; integral equation; Newton-Raphson approximation; LONGITUDINAL DATA; ADDITIVE-MODELS; POLYNOMIAL SPLINE; LINEAR-MODELS; TIME-SERIES; SELECTION; DYNAMICS;

D O I：

10.1214/12-AOS1026

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1906 / 1933

页数：28

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