Generalized Moment Estimation Model Average

Model averaging has become a hot topic in the field of statistics and econometrics,with its robustness and loss of less useful information.It has wide applications in many fields such as economics,finance,biology and medicine.As we all know,existing model averaging methods are based on the linear estimation mainly,but the research of model averaging based on the generalized method of moments(GMM)still has a lot of works to be done.One of the representative model averaging methods based on the linear estimation was proposed by Hansen in 2007.By optimizing Mallows criterion,he gets the best weights and opens the early research on the least squares model averaging.Hansen & Racine(2012)proposed a jackknife model averaging estimator which the weights were selected by minimizing a cross-validation criterion in heteroskedatic error settings.This estimator is demonstrated to be asymptotically optimal in the sense of achieving the lowest possible expected squared error.Since the estimation and prediction risk are directly affected by the quality of the weights,how to select weights becomes the most important question in the theoretical research of the model averaging.In this paper,we propose two kinds of model averaging methods under the GMM.Firstly,the weights are obtained by minimizing the J-fold cross validation criterion,and the asymptotic optimality of the model averaging estimator in the sense that it minimizes the squared estimation loss is proved.Secondly,the weights are obtained by minimizing the asymptotic mean square error of the average estimator of the target parameter.This method could make the average estimator more stable.These contributions have widened the existing research results on the model averaging theories.Both simulation results and empirical example show that the risk of our two kinds of GMM model averaging estimators are relatively low in most cases.