Empirical Likelihood For Linear Models With MA Errors

In this paper,empirical likelihood method,empirical Euclidean likelihood method and adjusted empirical likelihood method in statistics are used to analyze linear models with MA errors.First,we discuss the empirical likelihood inference of linear models with MA errors,and use the quasi-maximum likelihood method to obtain the estimation equation.Since the equation contains quadratic forms,in order to use the empirical likelihood method,martingale difference sequence is introduced to transform the quadratic forms into linear forms.Then the empirical likelihood ratio statistics of model parameters are constructed.Under certain assumptions,it is proved that the statistics obey chi-square distribution asymptotically,and the asymptotic confidence regions of the model parameters are obtained.Numerical simulation with R language verifies that the empirical likelihood method is superior to the traditional parametric likelihood ratio method in the coverage of confidence region.Secondly,we discuss the empirical Euclidean likelihood inference of linear models with MA errors,construct the empirical Euclidean likelihood ratio statistics of the model parameters and prove its asymptotic distribution,then the asymptotic confidence regions of the model parameters are obtained.Through numerical simulation,the conclusion is that the coverage of the confidence region obtained by the empirical Euclidian likelihood is slightly worse than that of the empirical likelihood.However,from the perspective of theoretical proof and calculation difficulty,the empirical Euclidean likelihood method is superior to empirical likelihood method.Finally,the adjusted empirical likelihood inference of linear models with MA errors is discussed,and the adjusted empirical likelihood ratio statistics of model parameters are constructed based on the empirical likelihood.It is proved that the proposed statistics are asymptotically subject to chi-square distribution,then the asymptotic confidence regions of the model parameters are obtained.Through numerical simulation,the adjusted empirical likelihood method is superior to the empirical likelihood method.