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Abstract:
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Model selection criteria often arise by constructing estimators of measures known as expected overall discrepancies. The expected overall Gauss (error sum of squares) discrepancy for a fitted linear model can be decomposed into a term representing the error due to estimation of unknown parameters and a term representing the approximation error, or bias, due to model misspecification. Since estimation error depends only on model dimension, a known quantity, the selection problem reduces to the problem of estimating the bias term for each fitted candidate model. In this talk, we consider various estimators, both frequentist and Bayesian, of bias for fitted linear models and consider how best to quantify the uncertainty inherent to a model selection problem. The most well known selection criterion within this framework is Mallows' Cp.
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