Which methods can utilize out-of-bag error to estimate test error?

Out-of-bag error is a technique used primarily in the context of ensemble methods, particularly bagging and random forests. It is a valuable tool because it allows for an unbiased estimate of the test error without needing a separate validation set.

In the case of bagging, which stands for bootstrap aggregating, multiple models are trained on different subsets of the training data created by resampling. Each model in the ensemble can be evaluated using the samples that were not included in its training set, providing a direct estimate of the model’s error on unseen data—this is known as the out-of-bag error.

Random forests, which are an extension of bagging that creates a collection of decision trees, also utilize out-of-bag error in a similar manner. Each tree is built using a bootstrap sample from the data, and the performance of these trees can be assessed using the observations that were not included in their respective samples. This makes random forests capable of estimating test error through out-of-bag error as well.

Boosting, on the other hand, does not rely on bootstrapping but rather works by sequentially training models in a manner where each new model focuses on the errors made by the previous ones. Boosting typically requires a separate validation