Generalized estimating equations are used in regression analysis of longitudinal data, where observations on each subject are correlated. Statistical analysis using such methods is based on the asymptotic properties of regression parameter estimators. This paper presents asymptotic results when either the number of independent subjects or the cluster sizes (the number of observations on each subject) or both go to infinity. A set of (information matrix based) general conditions is developed, which leads to the weak and strong consistency as well as the asymptotic normality of the estimators. Most of the results are parallel to the elegant work of Fahrmeir and Kaufmann on maximum likelihood estimators related to the generalized linear models. The conditions for weak consistency and asymptotic normality are verified for several examples of general interest.
"Asymptotics for generalized estimating equations with large cluster sizes." Ann. Statist. 31 (1) 310 - 347, Februrary 2003. https://doi.org/10.1214/aos/1046294467