SEMIPARAMETRIC GEE ANALYSIS IN PARTIALLY LINEAR SINGLE-INDEX MODELS FOR LONGITUDINAL DATA

In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equatio...

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Bibliographic Details
Published in:The Annals of statistics 2015-08, Vol.43 (4), p.1682-1715
Main Authors: Chen, Jia, Li, Degui, Liang, Hua, Wang, Suojin
Format: Article
Language:English
Subjects:
62G09
62G99
62H99
Asymptotic methods
Efficiency
Estimating techniques
GEE
Generalized linear models
local linear smoothing
longitudinal data
Monte Carlo simulation
Numerical analysis
Parameter estimation
semiparametric estimation
single-index models
Studies
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Summary:In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations (GEE) is introduced to estimate the two parameter vectors as well as the unknown link function. Under some mild conditions, we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios, from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data. We also discuss the estimation of the covariance (or weight) matrices involved in the semiparametric GEE method. Furthermore, we provide some numerical studies including Monte Carlo simulation and an empirical application to illustrate our methodology and theory.
ISSN:0090-5364
2168-8966
DOI:10.1214/15-AOS1320