Parameter Estimation And Variable Selection Of Partial Linear Model Based On Modal Regression

Partial linear model is an important semi-parametric statistical model.It includes two parts: parameters and smooth connection function.It not only has the advantages of ordinary linear model,but also is more flexible than linear model.Therefore,it has a wide range of applications in the statistical modeling of practical problems.Scholars also have very rich achievements in the research of this model.In this paper,the problem of parameter estimation and variable selection for partial linear models based on modal regression is studied.Firstly,compared with the local polynomial method,we adopt the common B-spline approximation for the nonparametric part;secondly,because of the particularity of modal regression,it obtains the robustness of the estimator by controlling the bandwidth of the kernel function,so we need to choose the appropriate bandwidth to realize the parameter estimation;finally,in the process of parameter solving,the statistical software packages can not solve the problem directly,so we need to use EM algorithm and iterate many times to get satisfactory results.The results of this study are mainly divided into two parts:Firstly,for the general partial linear model,we obtain the convergence rate of the estimation of parameters and nonparametric connection functions based on modal regression,and we validate the effectiveness of the method by Monte Carlo simulation.This method was applied to analyze the effects of various factors on plasma beta-carotene level,and the practical results are obtained.Secondly,we consider the variable selection problem of partial linear model based on modal regression.By using SCAD penalty,the convergence rate of parameter and nonparametric connection function estimation is also obtained,and variable selection is successfully realized.Monte Carlo simulation results show that the proposed method is effective.The model and method were also applied to analyze the effects of various factors on plasma beta-carotene level.After eliminating redundant variables,the model has better explanatory power.