Study On Some Problems Of Partial Linear Single Index Model With Longitudinal Data

In this paper,we focus on the longitudinal data,study the robust estimation of some linear single-index model and its variable selection.The main contents are as follows:Firstly,under the longitudinal data,a partial quartile method is used to estimate the connection function based on the robust quantile regression method.Under certain conditions,it is proved that the obtained estimator has asymptotic normality,and the implementation steps of the estimation algorithm are given.Through the numerical simulation analysis,the estimation effect of the regression function of different points is compared,and the robustness and validity of the proposed method are verified.Case study of Boston house price data,and further illustrates the practical application of the proposed method.Secondly,based on the LASSO and ALASSO double adaptive penalty estimation methods,a robust likelihood function is proposed.For the longitudinal data,the joint robust variable selection of the fixed effect and the random effect under the single linear linear mixed effect model is studied.Approximation method for the single index part of the unknown connection function to take the penalty spline approach.Under some regularization conditions,it is proved that the penalty is robust to the estimated Oracle properties.In the simulation study,the effect of the method is compared with that of the pollution and non-polluting data.The results show that the proposed method is robust.An example of the analysis of a group of CD4 data,the results obtained by the proposed method of effectiveness and practicality.