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Abstract:
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Theoretical properties of the conventional linear model are based on three strong assumptions, namely linearity, homoscedasticity and normality. Assuming fixed design, predictive risk estimates are often used as model selection criteria. However, in most cases, the three assumptions are rarely satisfied and random design should be included. The model selection procedure thus needs to be re-scrutinized. One of the widely used criterion is Mallows’ Cp which is only valid under fixed design and correctness of the full model. Under few assumptions, i.e., model lean framework, we 1) justify the least squared estimators 2) propose Generalized Cp (GCp) to estimate the prediction risk as a model selection criterion 3) derive the asymptotic properties of GCp. Simulation study also shows the drastic difference between Mallows’ Cp and GCp under model misspecification.
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