Fall Seminar Series - October 9, 2003
University of
Minnesota
School of Statistics
College of Liberal
Arts
Model Selection and Model Combining in
Regression
Yuhong Yang
Department of Statistics
Iowa State University
Thursday, October 9, 2003
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
There are a number of model selection criteria. In general, they work
well under different conditions or from different considerations. For example,
AIC is minimax-rate adaptive in terms of estimating the regression function
for both parametric and nonparametric settings and BIC is consistent in
terms of selecting the true model in a parametric setting. There are several
successful efforts in constructing more sophisticated model selection methods
to share the strengths of AIC and BIC in certain sense. However, we show
that the aforementioned essential properties of AIC and BIC cannot be combined
by any model selection procedure.
In recent years, methods have been proposed to combine models. We compare
model selection and model combining methods. The results support the view
that when model selection instability is low, model selection methods should
be preferred and when model selection instability is high, model combining
produces much more accurate estimators of the regression function.