2010/12/03 by Lan Wang · 110 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Asymptotic analysis #Asymptotic distribution #Binary data #Binary number #Consistency (knowledge bases) #Consistent estimator #Covariate #Delta method #Discrete mathematics #Estimating equations #Estimator #Generalized estimating equation #Mathematics #Minimum-variance unbiased estimator #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #math.ST #stat.TH
paper · pdf · doi:10.1214/10-aos846
published in The Annals of Statistics 39(1) (Institute of Mathematical Statistics) · 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)
openalex publication_date 2010/12/03 · arxiv created 2011/03/09 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.