GEE analysis of clustered binary data with diverging number of covariates

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.

Published in at http://dx.doi.org/10.1214/10-AOS846 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• Nonconcave penalized likelihood with a diverging number of parameters
• On the adaptive elastic-net with a diverging number of parameters
• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery
• Extending the scope of empirical likelihood
• GEE analysis of clustered binary data with diverging number of covariates
• Asymptotic results with generalized estimating equations for longitudinal data

Cited by in corpus (14)

• GEE analysis of clustered binary data with diverging number of covariates
• Semiparametric GEE analysis in partially linear single-index models for longitudinal data
• On Oracle Property and Asymptotic Validity of Bayesian Generalized Method of Moments
• Tensor Generalized Estimating Equations for Longitudinal Imaging Analysis
• A Revisit to De-biased Lasso for Generalized Linear Models
• High-dimensional generalized semiparametric model for longitudinal data
• Robust approach for variable selection with high dimensional Logitudinal data analysis
• On the Phase Transition of Wilk's Phenomenon
• Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates
• Wilks' theorems in some exponential random graph models
• Simultaneous Model Selection and Estimation for Mean and Association Structures with Clustered Binary Data
• Strong consistency and optimality for generalized estimating equations with stochastic covariates
• A sparse $p_0$ model with covariates for directed networks
• De-biased Lasso for Generalized Linear Models with A Diverging Number of Covariates