Limit Of The Optimal Weight In Model Averaging With Non-nested Models And A Discret Weight Set

In the past two decades,model averaging has become an important forecasting method in the fields of statistics and econometrics,and has received extensive attention from researchers.Most of the early research on model averaging methods focused on the Bayesian perspective,but later more and more experts and scholars began to pay attention to the frequentist model averaging.With regard to the method of frequentist model averaging,the classical theoretical work mainly focuses on the model weight selection criterion and the proof of asymptotic optimality.However,in recent years,the study of asymptotic limits of the optimal weight and model averaging estimator has become increasingly important.Most of the existing literatures are based on the nested model framework when studying the asymptotic distribution theory of optimal weights,and it is quite challenging to generalize existing results to non-nested models.In this paper,based on the framework of non-nested models,we derive the asymptotic limit of optimal weights averaged by least squares models in the case that all candidate models are likely to underfit,and then generalize this theoretical result to the model averaging method of logistic regression.Specifically,we define a subset M that satisfies certain conditions,proving that the optimal weights averaged by least squares or logistic regression models will asymptotically concentrated on candidate models within this subset superior.In addition to this,we also discuss some eligible subsets M.The method we mentioned in the paper and the obtained theoretical results can provide new ideas for studying the model averaging problem in the non-nested framework.Finally,we have performed a number of numerical simulations under different model settings,and the experimental results make the correctness of our theoretical results well verified.