The Covariance Inflation Criterion for Model Selection

                  Robert Tibshirani

Dept of Health Research & Policy and Dept of Statistics

                   Stanford University


I propose a new criterion for model selection in prediction
problems.  The covariance inflation criterion adjusts the training
error by the average covariance of the predictions and responses,
when the prediction rule is applied to permuted versions of the
dataset.  This criterion can be applied to general prediction
problems (for example regression or classification), and to general
prediction rules (for example stepwise regression, tree-based models
and neural nets).  As a byproduct we obtain a measure of the
effective number of parameters used by an adaptive procedure.  I
relate the covariance inflation criterion to other model selection
procedures and illustrate its use in some regression and
classification problems.  I also revisit the conditional bootstrap
approach to model selection.

This is joint work with Keith Knight.