Variable Selection In Single-index Varyingcoefficient Model For Longitudinal Data

Longitudinal data has the characteristics of "independent among groups and related within groups".It can reflect the differences between individuals and the changes within individuals.In the fields of medicine,epidemiology,industry,etc.,it has become a key issue for statisticians.With the rapid development of science and technology,the observed data has higher dimensions and more complex data structures.This requires more flexible models to fit complex data.Considering that the single-index varying coefficient model is a very important and attractive model in the semi-parametric model,it can not only reduce the risk of incorrect setting of the model,but also overcome the "curse of dimensionally " that cannot be overcome by non-parametric.Although there have been many literature studies on variable selection of longitudinal data,there are few studies on the problem of single-index varying coefficient models.Therefore,it is of great theoretical significance and use value to study the variable selection problem of the single index varying coefficient model under longitudinal data.Based on the single index varying coefficient model,this paper considers the situation of longitudinal data and variables selection for the model.For the problem that the model contains longitudinal data,there are various processing methods.This article will use the B-spline method to estimate the parameters of the model.At the same time,SCAD penalty will be used for variable selection.This paper combines the two methods as the statistical inference method needed in this paper.The content of this article is as follows:The first chapter mainly introduces the research background and significance of the model,the research status of the model,the types of data existence,and the method of variable selection.Finally,it introduces the structure of the full text and the research content and ideas.The second chapter first gives the form of the single-index variable coefficient model for longitudinal data and the basic assumptions of the model.Then it introduces some preliminary knowledge,including methods of variable selection,such as LASSO method,SCAD penalty method,and longitudinal data processing method.In the third chapter,under some assumptions,the SCAD penalty function is used to regularize the single index variable coefficient model under longitudinal data.Then,some theoretical properties of the model in the process of variable selection are given,including the consistency of parameter estimation and regularization estimation.Chapter 4,numerical simulation research,evaluates the effect of model selection using SCAD penalty method through Monte Carlo simulation,and based on adaptive sample adjustment parameters(ATP)and fixed parameter adjustment(CTP)under different sample sizes The comparison of the effect of variable selection leads to the following conclusions: First,when the sample size is unchanged,the estimated value of the parameter with a value of zero is correctly estimated as 0 and the value of a parameter with a value of non-zero is incorrectly estimated as 0 The averages of the numbers are close to the real situation.Second,as the sample size increases,the estimation error gradually decreases.Third,as the sample size increases,ATP-based variable selection methods are more effective than CTP-based variable selection methods.Simulations show that the results of this study are valid.