Mallows's Cp

In statistics, Mallows's ${\textstyle {\boldsymbol {C_{p}}}}$ ,^[1]^[2] 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 C_p has been shown to be equivalent to Akaike information criterion in the special case of Gaussian linear regression.^[3]

^ Mallows, C. L. (1973). "Some Comments on C_P". Technometrics. 15 (4): 661–675. doi:10.2307/1267380. JSTOR 1267380.
^ Gilmour, Steven G. (1996). "The interpretation of Mallows's C_p-statistic". Journal of the Royal Statistical Society, Series D. 45 (1): 49–56. JSTOR 2348411.
^ Boisbunon, Aurélie; Canu, Stephane; Fourdrinier, Dominique; Strawderman, William; Wells, Martin T. (2013). "AIC, C_p and estimators of loss for elliptically symmetric distributions". arXiv:1308.2766 [math.ST].

[1] Mallows, C. L. (1973). "Some Comments on C_P". Technometrics. 15 (4): 661–675. doi:10.2307/1267380. JSTOR 1267380.

[2] Gilmour, Steven G. (1996). "The interpretation of Mallows's C_p-statistic". Journal of the Royal Statistical Society, Series D. 45 (1): 49–56. JSTOR 2348411.

[3] Boisbunon, Aurélie; Canu, Stephane; Fourdrinier, Dominique; Strawderman, William; Wells, Martin T. (2013). "AIC, C_p and estimators of loss for elliptically symmetric distributions". arXiv:1308.2766 [math.ST].

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