Model Averaging Under Flexible Loss Functions

TL;DR

This paper introduces a flexible model averaging approach that optimally combines models under various loss functions, including asymmetric ones, using cross-validation to determine weights, and demonstrates its superior performance through simulations and real data.

Contribution

It develops a novel model averaging method that handles a wide range of loss functions, with proven asymptotic optimality and convergence properties.

Findings

Proposed method outperforms existing model selection and averaging techniques.

Establishes asymptotic optimality and convergence of model weights.

Demonstrates superior empirical performance through simulations and real data.

Abstract

To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other asymmetric/symmetric loss functions as special cases. The flexible loss function allows the proposed method to average a large range of models, such as the quantile and expectile regression models. To determine the weights of the candidate models, we establish a J-fold cross-validation criterion. Asymptotic optimality and weights convergence are proved for the proposed method. Simulations and an empirical application show the superior performance of the proposed method, compared with other methods of model selection and averaging.