Empirical Likelihood Inference For The Error Variance In Linear Regression Models Under Random Design

In chapter 2 of this paper,empirical likelihood estimation of error variance in linear regres-sion model when covariates are random is studied by using empirical likelihood method under the mechanism of random absence(MAR)of response variables.Under certain conditions,the asymp-totic normality of the estimator is proved,and the asymptotic variance of the estimator is smaller than that of the traditional least squares estimator when the error distribution is asymmetric.In chapter 3 of this paper,empirical likelihood ratio statistics of error variance in linear regression model when covariates are random is constructed When additional information is not utilized and additional information is utilized.The asymptotic distribution of the above two likelihood ratio statistics is proved to be chi-square distribution,and the empirical likelihood confidence interval of the error variance in this model is constructed.And considering the category test problem,it is proved that at the same test level the asymptotic efficacy of the test with additional information is higher than that without additional information when the error distribution is asymmetric.