  We study how to perform tests on samples of pairs of observations and
predictions in order to assess whether or not the predictions are prudent.
Prudence requires that that the mean of the difference of the
observation-prediction pairs can be shown to be significantly negative. For
safe conclusions, we suggest testing both unweighted (or equally weighted) and
weighted means and explicitly taking into account the randomness of individual
pairs. The test methods presented are mainly specified as bootstrap and normal
approximation algorithms. The tests are general but can be applied in
particular in the area of credit risk, both for regulatory and accounting
purposes.
