Empirical Likelihood Estimators Of The Error Variance In Nonparametric Models

Statistical circles has been paying attention to the field of nonparametric statistical inference.It has been widely applied in many fields,such as society,medicine,biology,psychology,peda-gogy and so on.Empirical likelihood is a nonparametric statistical inference method proposed by Owen^[18],this method has many advantages over its counterparts like the normal-approximation-based method and the bootstrap method.Consider the following nonparametric regression model Y=g?x?+e,where g?·?is the unknown mean function E?Y|x?,x??0,1?^p is fixed design points,Y is response variables,e is random variables with E?e?=0 and V ar?e?=?²>0.In this paper,we study the estimation of the error variance in nonparametric model under the fixed design.We given two estimators of error variance,one is the traditional method based on the residual sum of square,the other is the method based on the empirical likelihood.We also prove the asymptotic normality of the two estimators.Through data simulation,we find the asymptotic variance of the estimator that use empirical likelihood method is smaller than the asymptotic variance of the estimator that use the residual sum of square method.