GEE ANALYSIS OF CLUSTERED BINARY DATA WITH DIVERGING NUMBER OF COVARIATES

• 成果类型: Article
• 署名作者: Wang, Lan
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS846
• 发表日期: 2011
• 页码: 389-417
• 关键词: p-regression parameters; estimating equations; asymptotic-behavior; M-ESTIMATORS; semiparametric regression; robust regression; longitudinal data; linear-models; likelihood; inference

摘要

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) 310347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522-541] in the fixed p setting.