Prediction of quantiles at extreme tails is of interest in numerous
applications. Extreme value modelling provides various competing predictors
for this point prediction problem. A common method of assessment of a set
of competing predictors is to evaluate their predictive performance in a given
situation. However, due to the extreme nature of this inference problem, it can
be possible that the predicted quantiles are not seen in the historical records,
particularly when the sample size is small. This situation poses a problem to
the validation of the prediction with its realisation. In this article, we propose
two non-parametric scoring approaches to assess extreme quantile prediction
mechanisms. The proposed assessment methods are based on predicting a sequence of equally extreme quantiles on different parts of the data. We then
use the quantile scoring function to evaluate the competing predictors. The
performance of the scoring methods is compared with the conventional scoring method and the superiority of the former methods are demonstrated in a
simulation study. The methods are then applied to reanalyse cyber Netflow
data from Los Alamos National Laboratory and daily precipitation data at a
station in California available from Global Historical Climatology Network.