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August 2015 Semiparametric GEE analysis in partially linear single-index models for longitudinal data
Jia Chen, Degui Li, Hua Liang, Suojin Wang
Ann. Statist. 43(4): 1682-1715 (August 2015). DOI: 10.1214/15-AOS1320


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.


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Jia Chen. Degui Li. Hua Liang. Suojin Wang. "Semiparametric GEE analysis in partially linear single-index models for longitudinal data." Ann. Statist. 43 (4) 1682 - 1715, August 2015.


Received: 1 May 2014; Revised: 1 February 2015; Published: August 2015
First available in Project Euclid: 17 June 2015

zbMATH: 1317.62036
MathSciNet: MR3357875
Digital Object Identifier: 10.1214/15-AOS1320

Primary: 62G09 , 62G99 , 62H99

Keywords: efficiency , GEE , local linear smoothing , longitudinal data , Semiparametric estimation , Single-index models

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 4 • August 2015
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