# How to estimate the standard error of the leave-one-out cross-validation estimate of the prediction error?

How does one estimate the standard error of the leave-one-out cross-validation estimate of the prediction error?

For each fold (leave out the $i^{th}$ observation), the LOOCV estimate of the prediction error is

$(y_i-\hat{f}^{-i}(x_i))^2$

So the LOOCV estimate of the prediction error is the average over all $N$ folds

$\frac{1}{N}\sum_{i=1}^N(y_i-\hat{f}^{-i}(x_i))^2$

But how should I calculate the standard error of this estimate? I read that this standard error should be high relative to that of a K-fold CV where K = 5 or 10.