Semiparametric Mean-Covariance Regression Analysis for Longitudinal Data

Leng, Chenlei and Zhang, Weiping and Pan, Jianxin (2009) Semiparametric Mean-Covariance Regression Analysis for Longitudinal Data. [MIMS Preprint]

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E±cient estimation of the regression coe±cients in longitudinal data anal- ysis requires a correct speci¯cation of the covariance structure. Existing ap- proaches usually focus on modeling the mean with speci¯cation of certain co- variance structures, which may lead to ine±cient or biased estimators of pa- rameters in the mean if misspeci¯cation occurs. In this paper, we propose a data-driven approach based on semiparametric regression models for the mean and the covariance simultaneously, motivated by the modi¯ed Cholesky de- composition. A regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covari- ance. The resulting estimators for the regression coe±cients in both the mean and the covariance are shown to be consistent and asymptotically normally dis- tributed. In addition, the nonparametric functions in these two structures are estimated at their optimal rate of convergence. Simulation studies and a real data analysis show that the proposed approach yields highly e±cient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.

Item Type: MIMS Preprint
Uncontrolled Keywords: Covariance misspecification; Efficiency; Generalized estimating equation; Longitudinal data; Modified Cholesky decomposition; Semiparametric models
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User: Ms Lucy van Russelt
Date Deposited: 09 Jul 2009
Last Modified: 08 Nov 2017 18:18

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