Mallow’s Cp Statistic
- is used to access the fit of a linear regression model that has been estimated using ordinary least squares (aka ordinary least squares regression)
- has been shown to be equivalent to Akaike’s Information Criterion (AIC) in the special case of Gaussian linear regression
Mallow’s Cp Statistic - Definition
The 𝐶𝑝 statistic is defined as:
where:
- 𝑦 is the response vector
- 𝑋 is the design matrix
- 𝛽ˆ is the estimated parameters
- 𝑝 is the number of regressors/predictors (including the bias predictor)
- 𝑛 is the sample size
- 𝜎2 is the residual variance (if unknown it can be replaced with “best” estimate using full model)