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We consider two issues involved in model selection.
(1) Model selection starts with a proposed model class, and it is often
unrealistically assumed that the true model generating the data belongs
to this model class.
Then what would happen to model selection if the true model is not in
the proposed model class? In other words, how to quantify the model
selection bias in the situation of model class mis-specification?
(2) Model selection often ends up with a selected optimum model
minimizing or maximizing a numeric selection criterion function. But it
does not or is not able to provide a measure of variability or
uncertainty involved in model selection. Such a measure, if available,
would be very useful in determining models which are indistinguishable
from the optimum model.
We have developed new estimators of Kullback-Leibler information to
address these two issues. Our work will be presented in the context of
logistic regression model selection but can be extended to other model
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