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When evaluating and comparing models using leave-one-out cross-validation(LOO-CV), the uncertainty of the estimate is typically assessed using thevariance of the sampling distribution. Considering the uncertainty isimportant, as the variability of the estimate can be high in some cases. Animportant result by Bengio and Grandvalet (2004) states that no generalunbiased variance estimator can be constructed, that would apply for anyutility or loss measure and any model. We show that it is possible to constructan unbiased estimator considering a specific predictive performance measure andmodel. We demonstrate an unbiased sampling distribution variance estimator forthe Bayesian normal model with fixed model variance using the expected logpointwise predictive density (elpd) utility score. This example demonstratesthat it is possible to obtain improved, problem-specific, unbiased estimatorsfor assessing the uncertainty in LOO-CV estimation.

Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance