Empirical Likelihood Estimators Of The Error Variance In Partially Linear Models

Since Owen systematically established empirical likelihood methods for non-parametric cases,empirical likelihood methods have been widely used in various statistical models and have important application values in many fields such as social,economic,medical and so on.Partially linear model is a very significant model in statistics.It has extensive application and practice in many fields.In 1986,Engle et al.first proposed a partially linear model when studying the practical problem of the relationship between electricity and weather.Because the part of Partially linear models contains both parameters and non-parameters,it is easy to explain the influence of each variable,so it is more flexible and practical than the linear model in practical applications.The applicability and effectiveness of the partially linear model has attracted many experts and scholars to study the estimation and nature of parameters and non-parameters in the models.This paper mainly applies the empirical likelihood estimation method to the partially linear models.We apply the empirical likelihood method to propose a new class of model to estimate the error variance.Under certain regular conditions,the asymptotic normality of the traditional estimation of residual square sums and the empirical likelihood estimation proposed in this paper for error variance are proved.At the same time,the asymptotic variance of the empirical likelihood estimation and the asymptotic variance of the traditional method based on the sum of squares of residuals are obtained.The main content of this article is: Chapter 1 is an introduction.It briefly introduces the research of empirical likelihood method,error variance and partially linear models,as well as the content and innovation of this paper.The main results of this paper are given in Chapter 2.We use the empirical likelihood method to estimate the error variance in partially linear models,and prove the asymptotic normality of two estimates of the error variance in partially linear models under the fixed design situation.And the asymptotic variance of the empirical likelihood estimation and the asymptotic variance of the traditional method based on the sum of squares of residuals are obtained.At the same time,we also give the simulation results.From the simulation results,the empirical likelihood estimation method of the proposed error variance is superior to the traditional error variance estimation method.The innovation of this article is:1.For the first time,the estimation of the error variance in partially linear models under fixed design is studied.The traditional method based on the sum of squares of residuals and the empirical likelihood method are given.2.The asymptotic normality of the above two estimations of the error variance in partially linear models under the fixed design situation is proved,and the asymptotic variance of the empirical likelihood estimation and the traditional square sum of residuals are obtained.The asymptotic normality of two estimations of the error variance of the partial linear models under the fixed design situation is proved,and the asymptotic variance of the empirical likelihood estimation and the traditional method based on the sum of squares of residuals are obtained.From the simulation results,the empirical likelihood estimation method of the proposed error variance is superior to the traditional error variance estimation method.