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February 2011 GEE analysis of clustered binary data with diverging number of covariates
Lan Wang
Ann. Statist. 39(1): 389-417 (February 2011). DOI: 10.1214/10-AOS846

Abstract

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this “large n, diverging p” framework, we provide appropriate regularity conditions and establish the existence, consistency and asymptotic normality of the GEE estimator. Furthermore, we prove that the sandwich variance formula remains valid. Even when the working correlation matrix is misspecified, the use of the sandwich variance formula leads to an asymptotically valid confidence interval and Wald test for an estimable linear combination of the unknown parameters. The accuracy of the asymptotic approximation is examined via numerical simulations. We also discuss the “diverging p” asymptotic theory for general GEE. The results in this paper extend the recent elegant work of Xie and Yang [Ann. Statist. 31 (2003) 310–347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522–541] in the “fixed p” setting.

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Lan Wang. "GEE analysis of clustered binary data with diverging number of covariates." Ann. Statist. 39 (1) 389 - 417, February 2011. https://doi.org/10.1214/10-AOS846

Information

Published: February 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1209.62138
MathSciNet: MR2797851
Digital Object Identifier: 10.1214/10-AOS846

Subjects:
Primary: 62F12
Secondary: 62J12

Keywords: clustered binary data , generalized estimating equations (GEE) , High-dimensional covariates , sandwich variance formula

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 1 • February 2011
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