Mallows's Cp - Wikipedia

The Cp statistic is often used as a stopping rule for various forms of stepwise regression. Mallows proposed the statistic as a criterion for selecting among many alternative subset regressions. Under a model not suffering from appreciable lack of fit (bias), Cp has expectation nearly equal to P; otherwise the expectation is roughly P plus a positive bias term. Nevertheless, even though it has expectation greater than or equal to P, there is nothing to prevent Cp P or even Cp 0 in extreme cases. It is suggested that one should choose a subset that has Cp approaching P,[6] from above, for a list of subsets ordered by increasing P. In practice, the positive bias can be adjusted for by selecting a model from the ordered list of subsets, such that Cp 2P. Since the sample-based Cp statistic is an estimate of the MSPE, using Cp for model selection does not completely guard against overfitting.