Gee Analysis Of Non-Negative High-Dimensional Longitudinal Data

Generalized linear model (GLM) as an important extension of the classical linear model is suitable not only for continuous data but also for discrete data, in particular for the latter, for example categorical data and counted data. On the other hand, the Longitudinal data is that observations on each subject are correlated and observations on the different subjects are independent. Recently, the generalized estimating equation (GEE) introduced by Liang and Zeger have attracted a lot of interest. They are mainly applied to the regression analysis of longitudinal data. Some new results about them have been established during the past years.The main aim of the paper is to prove the large sample theory, such as the consistency, and asymptotic normality, of GEEs in the Gamma distribution models with the canonical link functions via using Cauchy-Schwarz Inequality and Limit Theory of Probability, especially the technique of the existence theorem of multivariate nonlinear equations root, when the simple sizes nâ†'∞, and the dimension of covariates pnâ†'∞.