Fall 2008 Thursday, October 9   Speaker: Yuhong Yang School of Statistics University of Minnesota "Consistency and Optimal Estimation with Model Selection/combination". Abstract: When multiple models/procedures are considered, finding the true or best candidate is a natural goal. The concept of consistency in selection was developed accordingly. When cross-validation is employed for model selection, we show that there is a drastic difference between comparison of parametric regression models and comparison of general regression procedures. Implications on real applications will be discussed. Asymptotically optimal estimators/predictions based on a true parametric model can sometimes be much improved. This is especially the case in quantile regression at extreme probability levels, which then calls for a consideration of alternative methods such as semi-parametric and non-parametric ones. In this context, we develop a model/procedure combining method and obtain an oracle risk bound without any parametric assumption. At each given probability level, the combined quantile estimator is shown to perform almost as well as the best candidate, which often results in a substantial improvement in accuracy over the best candidate in a global performance measure. Examples will be provided to demonstrate advantages of the combination approach. And here are a couple links to relevant papers: http://www.stat.umn.edu/~yyang/papers/ShanYang.pdf http://www.stat.umn.edu/~yyang/papers/Cv_19.pdf

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