Jackknife model averaging for mixed-data kernel-weighted spline quantile regressions

Abstract

In the past two decades, model averaging has attracted more and more attention and is regarded as a much better tool to solve model uncertainty than model selection. Compared with the conditional mean regression, the quantile regression serves as a robust alternative and shows a lot more information about the conditional distribution of a response variable. In this paper, we propose a jackknife model averaging procedure that chooses the weights by minimizing a leave-one-out cross-validation criterion function for mixed-data kernel-weighted spline quantile regressions that contain both continuous and categorical regressors when all candidate models are potentially misspecified. We demonstrate the JMA estimator is asymptotically optimal in terms of minimizing the out-of-sample final prediction error. Simulation experiments are conducted to assess the relative finite-sample performance of the proposed JMA method with respect to other model selection and averaging methods. Our JMA method is applied to the wage and house datasets.