Which of the following statements is true about the statistics AIC, BIC, and Mallow's Cp?

The choice indicating that models with smaller values of AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), and Mallow's Cp are desirable is accurate. These statistics are specifically designed to evaluate the quality of statistical models while considering both their fit to the data and their complexity. A smaller value for any of these criteria typically indicates a better model: it shows that the model fits the data well while also being less complex, which is crucial in avoiding overfitting.

AIC and BIC are based on likelihood functions and include a penalty for the number of parameters to discourage the use of overly complex models. Mallow's Cp serves a similar purpose in assessing model fit against the number of predictors used, with a Cp value closer to the number of parameters indicating a well-fitted model without overfitting. Therefore, aiming for the lowest possible values of these criteria helps in selecting a model that achieves an optimal balance between goodness-of-fit and model simplicity, which is a fundamental principle in statistical modeling.