To determine which method is not an example of an indirect approach to estimating test Mean Squared Error (MSE), we need to understand each of the approaches listed:
1. Adjusted R-squared: This is a statistical measure that adjusts the regular R-squared for the number of predictors in a model. It is used to determine the proportion of the variance for a dependent variable that's explained by independent variables in a regression model, adjusted for the number of predictors. It is an indirect measure used in model selection.
2. Mallow's Cp: This is a criterion that provides a trade-off between bias (accuracy) and precision (variance) in the selection of predictive models. It is also an indirect estimate of the model quality.
3. BIC (Bayesian Information Criterion): This criterion is used for model selection among a finite set of models; it is based on the likelihood function and includes a penalty term for the number of parameters in the model to prevent overfitting. It is another type of indirect approach.
4. AIC (Akaike Information Criterion): Similar to the BIC, this criterion estimates the quality of each model, relative to each of the other models. It is used for model selection and also includes a penalty term for the number of parameters. This is an indirect approach.
5. k-Fold Cross-Validation (k-Fold CV): This method is a direct approach to estimating test MSE. It involves partitioning the sample into k subsets, training the model k times, each time using a different subset as the test set and the remaining k-1 subsets as the training set. The results are averaged to produce a single estimation.
Based on these explanations, k-Fold CV is the method that does not belong to the indirect approaches to estimating test MSE.
Thus, the correct answer is:
O k-Fold CV
