期刊
ANNALS OF STATISTICS
卷 39, 期 1, 页码 389-417出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/10-AOS846
关键词
Clustered binary data; generalized estimating equations (GEE); high-dimensional covariates; sandwich variance formula
资金
- NSF [DMS-1007603]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007603] Funding Source: National Science Foundation
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.
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