Optimal model averaging estimator for semi-functional partially linear models

There have been many papers on frequentist model averaging over the past decade, but very little attention has been paid to how to conduct frequentist model averaging in functional data analysis. The present paper considers 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 finite-sample performance of the proposed methods, and an empirical application with PM2.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{2.5}$$\end{document} data illustrates the proposed estimates.