Generalized Estimating Equation And Penalized Generalized Estimation Equation Analysis Of High Dimensional Longitudinal Data

Generalized linear model,an important model for dealing with discrete random variables,is of great significance to statistical analysis in various fields and can overcome the shortcomings of general linear model.The generalized estimating equation(GEE)and penalized generalized estimating equation(PGEE)for high dimensional longitudinal data in this article are extended on the basis of generalized linear models,is a statistical model for processing longitudinal data.They are applied more and more widely in real life,and with the continuous progress of science and technology,collecting more and more kinds of data,and the structure becomes more and more complex.Such data often appear in biomedical field.Therefore,(PGEE)GEE of high dimensional longitudinal data in this article can not be underestimated either in theory or in practice.Rather than linear model,which can only fit some special data,generalized linear model has greater flexibility and is used more and more widely.Wang(The Annals of Statistics,39(1):389-417)proves the consistency of correlation coefficient matrix estimates for generalized estimation equation of classical Logit model under weaker conditions.Based on this,In this article,under more weaker conditions,the consistency of correlation coefficient matrix estimates for GEE count data is proved,and the corresponding results in literature are extended.Wang et al.(Biometrics,68(2):353-360)has proved the asymptotic properties of estimators of penalized generalized estimating equation in classical Logit model under weaker conditions.However,for the two-stage logit model,Its connection function is not only a natural connection function,but also divides all observation objects into two categories according to their states,which are mainly divided into two steps:the first step is to divide the observation data of three states into two categories;The second step,in which each class is determined to be in its state.For example,the effect of drugs on patients is"good","unchanged","worse".Among them,"worse"is divided into one category and"unchanged","good"is divided into another category.Secondly,the PGEE is formed by adding a SCAD penalty to the GEE,Because the penalty has Oracle property,the predicted results are highly consistent with the real model.Its purpose is to eliminate redundant variables when selecting variables,so as to improve the accuracy of the model in practical application,thus the PGEE of the two-stage Logit model is established.Finally,by using Bernstein inequality and other theorems and properties,Under more weaker conditions prove the asymptotic properties of the estimators of PGEE for two-stage Logit model,the corresponding results in the literature are extended.It is also a further research of the asymptotic properties of the estimators of PGEE for classical Logit model.