Model Averaging For Nonlinear Models

Model averaging considers all candidate models by giving higher weights to the better models,which can obtain better performances of estimators and forecasts.The choice of model weights is the most important and challenging in model averaging.Optimal model averaging methods don't rely on the assumption that the true model is one of the candidate models.The aim of optimal model averaging methods is to reduce the predictive risk,and the resulting model averaging estimators are asymptotically optimal in the sense that they produce a loss that is asymptotically equivalent to that of an infeasible best-possible model averaging estimator.In the past decade,the researchers have done a lot of work on optimal model averaging methods for linear models.As the development of that,optimal model averaging methods for nonlinear models have received much interest,but there are still many widely used nonlinear models that have not been considered.Therefore,the aim of this thesis is to fill this gap,so that optimal model averaging methods can meet the needs of more applications.The concrete results are as follows:(1)A Kullback-Leibler loss based weight choice criterion for multinomial logit models is developed to determine averaging weights.When the candidate models do not contain the true model,we prove that the resulting model averaging estimators are asymptotically optimal.When the true model is one of the candidate models,the averaged estimators are consistent.Simulation studies suggest the superiority of the proposed method over commonly used model selection criterions,model averaging methods,as well as some other related methods in term of Kullback-Leibler loss and mean squared forecast error.Finally,an empirical application on the website phishing data illustrates the proposed method.(2)Considering on expectile regressions,we propose the J-fold cross-validation model averaging criterion to determine averaging weights.Not only can it improve the performance of forecasts,but also it can account for the instability of estimates and avoid ignoring the uncertainty introduced by the model selection procedure.When the candidate models do not contain the true model,we prove that the resulting model averaging estimators are asymptotically optimal in the sense that they produce an expectile loss that is asymptotically equivalent to that of an infeasible best-possible model averaging estimator.When the true model is one of the candidate models,the averaged estimators are consistent.Simulation experiments suggest that the proposed method is superior to the J-fold cross-validation model selection method,several information criterion-based model selection and averaging methods.Finally,an empirical application on the wage data illustrates the proposed method.(3)We consider an optimal model averaging estimator for a semi-functional partially linear model with heteroscedasticity.Mallows-type and generalized cross-validation weight choice criteria are developed to assign model averaging weights.Under some regular assumptions,the resulting model averaging estimators are proved to be asymptotically optimal.Simulation results demonstrate the superiority of the proposed methods over some other model selection and averaging strategies.Finally,an empirical application with PM_2.5data illustrates the proposed estimates.