Model Averaging In Composite Quantile Regression

In the regression estimation,the classical least squares estimation only focuses on the central part of the corresponding variables and its variation trend,so there is a certain limitation.In order to overcome this defect and fully understand the data,Roger Koenker proposed the quantile regression method in 1978.Compared with common mean regression,quantile regression is a method which estimate the parameters by minimize the weighted residual absolute sum.This method is able to describe the overall distribution of the data by setting different percentile points and has better performance especially when there is heteroscedastic data,or the model exists outliers,therefore this method has received extensive attention and deeper application.But the estimation efficiency of quantile regression is influenced by the value of the quantile point.Therefore,composite quantile regression is proposed.Based on quantile regression,the coefficients of regression are kept same at different quantile points,so as to further improves the estimation efficiency.Model averaging is a method that averaging the estimators or the predictions from different models,which is also called model combination.Compared with model selection,the model averaging method can avoid missing data information or the risk of deviation due to the wrong choice of models,which is more robust than the model selection method.It is an effective way to solve the uncertainty of model selection and reduce the error as well.In this paper,we introduce the theory and good properties of the composite quantile regression and model averaging method,furthermore,combine these two methods in the local misspecification framework to estimate parameter and predict related variables.The model averaging in composite quantile regression can guarantee the effective and robustness of the model in the case of the nonfinite variance of the random error term.At the same time,proving the asymptotic property of the submodel,which further ensure the validity of the estimated results after the averaging.At the end,comparison of the various kinds of data in the least squares method,median regression method,composite quantile model and averaging composite quantile regression model with different selection of weighting shows that the averaging composite quantile regression has lower mean square error and good performance especially when the random error term does not have finite variance,or the data has outliers.