The Annals of Statistics
- Ann. Statist.
- Volume 43, Number 4 (2015), 1682-1715.
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 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.
Ann. Statist., Volume 43, Number 4 (2015), 1682-1715.
Received: May 2014
Revised: February 2015
First available in Project Euclid: 17 June 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Chen, Jia; Li, Degui; Liang, Hua; Wang, Suojin. Semiparametric GEE analysis in partially linear single-index models for longitudinal data. Ann. Statist. 43 (2015), no. 4, 1682--1715. doi:10.1214/15-AOS1320. https://projecteuclid.org/euclid.aos/1434546219
- Supplement to “Semiparametric GEE analysis in partially linear single-index models for longitudinal data”. The supplement gives the proof of Theorem 3 and some technical lemmas that were used to prove the main results in Appendix B. It also includes some additional results of our simulation studies described in Section 5.