Empirical Likelihood Estimators Of The Error Variance In Linear Models

Empirical likelihood estimators is one of the fields that has been focused in statistics,and the problem that empirical likelihood estimators has a important application value in the social,economic,medical and other fields.We consider the estimators of the error variance in linear models what is a great significant research under the background of empirical likelihood method.We use empirical likelihood method to study a new error variance estimator problem in lin-ear model,and obtain the asymptotic estimators of the estimators.Under certain assumptions,we prove the asymptotic normality of the estimators,it is concluded that the estimators of the asymptotic variance is smaller than traditional estimators.Then,the main conclusions are verified by numerical simulation,and the effectiveness of the estimators presented in this paper and the effectiveness of traditional estimators is compared.The main contents are divided into three chapters:The first chapter is the introduction,briefly introduces the research overview between the empirical likelihood estimators of error variance in linear model and the traditional estimators,the research background and research progress of the empirical likelihood method,as well as the content and innovation points.In the second chapter,the traditional estimators are modified by the empirical likelihood method,and the asymptotic variance of the modified estimators is smaller than the asymptotic variance of the traditional estimators,and we give some assumptions and main results,simulation results,lemma and main results.The third chapter is the main conclusion and the prospect.The main results and innovation points can be summarized as follows:1.The estimators of linear model error variance with fixed design situation is studied by empirical likelihood method for the first time,and the asymptotic variance of this estimators is obtained.2.In this paper,the main conclusions are verified by numerical simulation,and comparing with the traditional estimators,the efficiency ofσ²_elrelative toσ_n²is less than 1.It shows that the variance of the linear model error variance of the fixed design situation that we’re using empirical likelihood method is less than the traditional estimatorsσ_n²variance.Therefore,the empirical likelihood estimators method greatly improve the estimators efficiency of the linear model error variance of the fixed design situation.