Frequentist Model Averaging: A General Framework and Theories

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Priyam Mitra*+ and Min-ge Xie and Hua Liang
• Companies: and Rutgers University and George Washington University
• Keywords: Model average estimators ; Bias variance trade-off ; Asymptotics ; MSE

Abstract

We propose a general framework for frequentist model averaging and study the asymptotic behavior of such estimators. The proposed framework broadens the scope of existing methodology by including models even with large biases. With the true model unknown, model averaging provides a way to account for model uncertainty inherent in model selection procedures. Assuming the data are from an unknown model, we derive the model average estimator and describe the limiting distributions and risk properties while taking potential modeling bias into account. We use a selection of weights to combine the individual stimators with the weights chosen so that they minimize an unbiased estimate of the mean square error of the model average estimator. To demonstrate this idea we use a linear regression framework and combine estimators from a set of candidate models and discuss its asymptotic properties. A simulation study is performed to compare the performance of the estimator with that of existing methods. The results show the benefits of incorporating multiple models in the estimator rather than a single one.