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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, March 21, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 p.m. in 1st Floor Lounge)}

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\centerline{\sl Yuhong Yang}
\centerline{\sl Department of Statistics}
\centerline{\sl Iowa State University}
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\centerline{\bf Model Selection, Model Averaging, and Adaptive Estimation}
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Model Selection has been widely studied in both theory and applications.
Estimators based on appropriately selected models have been theoretically
shown to be adaptive in the sense that they
automatically perform as well as if the best model were known in advance.
>From a practical point of view, however, model selection often causes
considerable instability in estimation, resulting in unnecessarily large
variance in the final estimator.
 
Model averaging provides an alternative to model selection. A
computationally feasible algorithm ARM rooted in information theory is
proposed to combine different models/procedures. It produces a convex
combination of the original estimators with data-dependent weights. 

The proposed algorithm ARM is shown to have the desired theoretical
capability of adaptation over different models and/or procedures. That is,
it automatically performs as well (or nearly so) as the best
model/procedure. Some simulations are conducted to compare its performance
with familiar model selection criteria and their stabilized versions based
on the bagging idea of Breiman (1996). The results show effectiveness of
ARM in both parametric and nonparametric settings. 

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