Mallows's C_p

In statistics, Mallows's ${\textstyle {\boldsymbol {C_{p}}}}$, named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares. It is applied in the context of model selection, where a number of predictor variables are available for predicting some outcome, and the goal is to find the best model involving a subset of these predictors. A small value of ${\textstyle C_{p}}$ means that the model is relatively precise.

Mallows's ${\displaystyle C_{p}}$ is 'essentially equivalent' to the Akaike information criterion in the case of linear regression. This equivalence is only asymptotic; Akaike notes that ${\displaystyle C_{p}}$ requires some subjective judgment in the choice of the variance estimate associated with each response in the linear model (typically denoted as ${\displaystyle {\hat {\sigma }}^{2}}$).