Outlier robust model averaging based on S_p criterion

Abstract

In this paper, we consider the problem of obtaining appropriate weights for model averaging in the face of model uncertainty and outliers. Most of the current model averaging methods are based on ordinary least squares (OLS) estimators, which are very sensitive to outliers or departures from the normality assumption on the error distribution. To overcome this problem, we propose an outlier robust Sp‐type model averaging (SMA) procedure whenever data contain outliers. The proposed method combines the advantages of model averaging and robust model selection. Therefore, it performs better than other classical model averaging and robust model section methods, especially in the outlier data case, and nearly the same as Mallows's model averaging (MMA) even in the clean data case. Moreover, the proposed criterion is quadratic in the weights, so it is operationally simple to implement. The performance of the proposed method is illustrated through some extensive simulation studies as well as real data examples.