9.6 Resampling methods (5): Leave-one-out cross-validation (LOOCV)

• In classification setting LOOCV error rate takes the form (James et al. 2013, 184):

\[CV_{(n)} = \frac{1}{n}\sum_{i=1}^{n}Err_{i}\] where \(Err_{i}=I(y_{i}\neq\hat{y}_{i})\), i.e., is 1 when \(y_{i}\) was wrongly predicted

• Linear regression: Use MSE rather than number of misclassified observations to quantify test error

• The k-fold CV error rate (see next slide) and validation set error rates are defined analogously

References

James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2013. An Introduction to Statistical Learning: With Applications in R. Springer Texts in Statistics. Springer.