Corrected Mallows criterion for model averaging

Abstract

An important problem with model averaging approach is the choice of weights. The Mallows criterion for choosing weights suggested by Hansen (2007) is the first asymptotically optimal criterion, which has been used widely. In the current paper, the authors propose a corrected Mallows model averaging (MMAc) method based on F distribution in small sample sizes. MMAc exhibits the same asymptotic optimality as Mallows model averaging (MMA) in the sense of minimizing the squared errors. The consistency of the MMAc based weights tending to the optimal weights minimizing MSE is also studied. The authors derive the convergence rate of the new empirical weights. Similar property for MMA and Jackknife model averaging (JMA) by Hansen and Racine (2012) is established as well. An extensive simulation study shows that MMAc often performs better than MMA and other commonly used model averaging methods, especially for small and moderate sample size cases. The results from the real data analysis also support the proposed method.