Quantile Regression Variable Selection In Some Models

Quantile regression has taken an import role to study the conditional distribution of the response variable. Variable selection also widely be used in industrial field. In this paper, we focus on quantile regression in complex situation, the medical cost data and the counts data. We use partial nonlinear single index model to model the medical cost data and jittering method to process counts data. Because of high dimensions, using adaptive LASSO to select the import variables. The performance of our method are illustrate by simulations and example analysis.For medical cost data, we will use PNSIM model to analysis, and get the estimation of coefficients by using two-stage method. Variable selection will be processed on this basis. First stage, we will use the two-step estimation method basing the splines to get the estimation of the nonparametric additive components. The estimation derived by the first step will be convergence by the speed of when the nonparametric additive components are-th differentiable, and the first step could overcome the difficulty caused by the curse of dimension. Second stage, we will get the estimations of coefficients and process the variable selection on the basis of first stage.For the counts data, we will construct a continuous random variable whose quantiles have a one-to-one relation with the quantiles of response variable to apply the standard quantile regression and variable selection.The paper is organized as follows.The first chapter is the literature review describes recent developments in the field, as well as related research scholars. And we will introduce our research content and innovation of this paper.The focus of the second chapter is using partial nonlinear single index model to model medical cost data, and using estimation method based on spline basis to get the estimation of coefficients, variable selection will be processed by adaptive LASSO penalty term on the basis. Finally, the simulation and example analysis will be presented to illustrate our method performance. The proof of asymptotic properties are presented at the end of the chapter.The third chapter is focused on quantile regression variable selection of discrete counts data. We will process the response variable to apply the standard quantile regression, and then process the variable selection by adaptive LASSO penalty term on the basis. In the end, the asymptotic properties of estimation will be proved.The fourth chapter gives a summary, and possible research directions can be researched in the future.In summary, this paper gives solutions of processing medical cost data and discrete counts data. The medical cost data can be model by the partial nonlinear single index model(PNSIM), and the discrete counts data can be analysis standard quantile and variable selection after processing the response variable by appropriate method. These method both overcome the difficulty caused by the curse of dimension. From the perspective of computational efficiency, the estimation of nonparametric additive components can be transform into solve of linear program, then the process of computing need less iterations. That will improve the performance of the two-stage method of partial nonlinear single index model.