I have a question concerning the one-standard-error rule when doing leave-one-out cross-validation.
firstly, my summary of the one-standard-error rule:
When using cross-validation or validation the model with the lowest test error will most likely change for every time the model is fitted with another random assignment of observations to the folds. Therefore, the one-standard-error rule can be used to select the simplest model that is within one standard error of the model with the lowest test error. The rational behind the rule is that, when there is, from a statistical point of view, not much difference between the models, why not choose the simplest model
Secondly, my question:
If the above "definition" holds, then there should be no standard error when applying leave-one-out cross-validation. The reason being that, the observations assigned to the folds are always the same, so there is no variance in the cross-validation error. Therefore, I wonder why RStudio and Matlab still give standard errors when LOOCV is applied?