Study On Some Problems Of Penalized Generalized Estimating Equation Based On Compound Order Model

The generalized estimating equation is a statistical model which is dedicated to processing longitudinal data.It is an extension based on the generalized linear model,which effectively solves the problem of correlation between response variables in longitudinal data,and obtains robust parameter estimates.However,the penalized generalized estimating equations adds penalized function based on the generalized estimating equations to perform variable selection and eliminates redundant variables.And it achieves the purpose of improving the accuracy of the model.This thesis mainly studies the penalized generalized estimating equations based on compound order model,and discusses the asymptotic property of penalized generalized estimating equations estimation.Firstly,this thesis introduces the compound order model and penalized generalized estimating equations.The compound order model is a generalization of the classical Logit model,so that it can deal with more complex attribute data.Due to the advantages of the compound order model in processing data,the penalized generalized estimating equations is established for processing high-dimensional longitudinal data with response variables as multi-category ordered attributes.Considering that the SCAD function has the property of Oracle,this thesis chooses SCAD penalized function as the penalized function.Secondly,under the framework of "big n,diverging p",this thesis improves the assumptions according to the selected model,explores with analytical methods,uses Cauchy-Schwarz inequality,absolute value inequality,the compatibility of norms and the like,and proves the asymptotic existence and consistency of the pre-s_n row of the compound order model generalized estimating equations estimation.Then,based on that,according to the definition of the SCAD penalized function and the penalized generalized estimating equations,by transforming the results with the help of means of full probability formulas and the property of probability,and employing Jensen's inequality,Bernstein's inequality,the asymptotic property of the penalized generalized estimating equations estimation is proved.Finally,this thesis explores the asymptotic normality of the penalized generalized estimating equations estimation based on the asymptotic existence and consistency.Splitting the results according to the asymptotic existence and Lagrange mean value theorem,this thesis uses the Rayleigh-Rize theorem,lindberg's central limit theorem and the like to prove that one of them converges to the standard normal distribution,and the others converge to zero in probability.And the asymptotic normality of the penalized generalized estimating equations estimation is proved according to Slutsky theorem.In addition,this thesis also studies the asymptotic property of the generalized estimating equations estimation when the number of individual observations tends to be infinite.The asymptotic property of generalized estimating equations estimation is proved by limiting the divergence speed of the number of observations.