Empirical Euclidean Likelihood Estimators Of The Error Variance In Partially Linear Models

Statistical inference is one of the important problems in mathematical statistics.We know that the distribution function can not be determined by the moments of each order,but the moments of each order can indirectly reflect some important information of distribution,especially when the distribution function is unknown.How to reasonably infer the numerical characteristics of population distribution or distribution according to samples is a problem to be solved in statistical inference,and the estimation of error variance of regression model is one of them.In the regression model,the traditional method of parameter estimation does not take into account the influence of each order moment of the sample on the estimation result,so that the information contained in each order moment of the sample is not fully reflected in the estimation process.In the case of empirical Euclidean likelihood method,the error variance in regression model is re-estimated with full consideration of the information contained in the moments of errors.In the case of fixed design,the asymptotic normality of the estimator is proved.The asymptotic variance of the new estimator is calculated and compared with the traditional error variance estimation method.The result shows that the asymptotic variance of the new estimator is smaller.