Least Squares Model Average Under LINEX Loss

In recent years,the application of model average method is becoming more and more widely,and it is a hot topic in the research of modern economy,biology,medicine and statistics.A good weight can minimize the risk of prediction or estimation to achieve the purpose of research.But a poor set of weights can lead to a large deviation in the estimation or prediction,and sometimes a great loss to the actual problem.So,how to select the combination weight is the most important and the most difficult problem in the actual research work.One of the most important contributions to this problem is Hansen(2007,Econometrica).By optimizing Mallows criterion,he gets the best weight and opens the early least squares model.The main contribution of Hansen's papers is to prove that the Mallows criterion is asymptotically equivalent to the squared error.Therefore,the minimization of the Mallows model minimizes the squared error in large samples.In this paper,we obtain a weight vector by minimizing a new criterion,and introduce a new model average method,and prove the asymptotic optimality of the estimation in discrete weight set and non nested model structure.In some estimation and prediction problems,use of symmetric loss functions may be inappropriate.Since the existing model average methods are all based on the symmetric loss,we introduce the method of selecting random weights on the asymmetric loss criterion,and the simulation and application results show the superiority of the estimation under this criterion.These contributions have widened the existing research results on the model averaging theory.