An outlier-robust model averaging approach by Mallows-type criterion

TL;DR

This paper introduces a robust model averaging method using a Mallows-type criterion that minimizes an expected prediction error estimator, effectively handling outliers with robust loss functions.

Contribution

It develops a novel outlier-robust model averaging approach based on a Mallows-type criterion, extending model averaging to be less sensitive to outliers.

Findings

Outperforms traditional methods in the presence of outliers

Demonstrates strong finite-sample performance through simulations

Effective on real data with outliers

Abstract

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function, which could be very sensitive to the presence of outliers in the data. In this paper, we propose an outlier-robust model averaging approach by Mallows-type criterion. The key idea is to develop weight choice criteria by minimising an estimator of the expected prediction error for the function being convex with an unique minimum, and twice differentiable in expectation, rather than the expected squared error. The robust loss functions, such as least absolute deviation and Huber's function, reduce the effects of large residuals and poor samples. Simulation study and real data analysis are conducted to demonstrate the finite-sample performance of our estimators and compare them with other model selection and averaging methods.