题目

Choice of Weights for Frequentist Model Averaging Estimators

报告人

Guohua Zou, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

时间

2010年4月27日（周二）下午2:00-3:00

地点

光华管理学院2号楼216

摘要

There has been increasing interest recently in model averaging within the frequentist paradigm. The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process. One of the most important, yet challenging, aspects of model averaging is how to optimally combine estimates from different models. Recently, Hansen (Econometrica, 2007) proposed to choose weights by minimizing a Mallows criterion. The main contribution of Hansen’s paper is a demonstration that the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen's approach. The first is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic from a practical viewpoint. Second, for the optimality result to hold, the model weights are required to lie within a special discrete set. In fact, Hansen noted both difficulties and called for an extension of the proof technique for the second assumption. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a nonnested set-up. Further, we also suggest a new model average estimator with weights selected by minimizing an approximate GCV criterion. Simulation and real data analysis show the good performance of the proposed estimator.

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