Penalized Generalized Estimating Equations For High-Dimensional Longitudinal Attribute Data Regression Analysis

Longitudinal data refers to the same cross-sectional units, for n times repeated observations and the cross section data with time series data of data, at different times, there have higher dimensional longitudinal data as covari-ate Pn tend to ∞,On the basis of the longitudinal data. Generalized estimating equation is widely used in regression analysis of longitudinal data. After the first referenced by Liang and Zeger, Generalized estimating equation made a great progress in the theory and also the practical application. This academic dissertation is based on the high dimensional longitudinal attribute data, and then analyzing the existence, consistency, sparse and asymptotic normality of the generalized estimating equations with the addition of punishment factor.First of all, on some certain conditions, as the response variable obeys the distribution of logistic, and the sample size n, association variable dimen-sion of Pn, all of these factors that I mentioned above tend to be infinity, then using Bernstein inequality, LQA-Newton-Raphson algorithms, as well as the existence theorem of nonlinear equations root to research the existence and the consistency of the punishment of generalized estimating equations.Secondly, on the basis of the study of Wang and some other schol-ars(Biometrics,2012,68:353-360),and study the conditions on the basis of the weakening, using Lindeberg center limit theorem to analyze the asymp-totic normality of punishment generalized estimating equations.