Least Squares Model Averaging

This paper considers the problem of selection of weights for averaging across leastsquares estimates obtained from a set of models. Existing model average methods are based on exponential AIC and BIC weights. In distinction, this paper proposes selecting the weights by minimizing a Mallows ’ criterion, the latter an estimate of the average squared error from the model average fit. We show that our new Mallows ’ Model Average (MMA) estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators. In a simulation experiment we show that the MMA estimator compares favorably with those based on AIC and BIC weights. The proof of the main…