  We study tail estimation in Pareto-like settings for datasets with a high
percentage of randomly right-censored data, and where some expert information
on the tail index is available for the censored observations. This setting
arises for instance naturally for liability insurance claims, where actuarial
experts build reserves based on the specificity of each open claim, which can
be used to improve the estimation based on the already available data points
from closed claims. Through an entropy-perturbed likelihood we derive an
explicit estimator and establish a close analogy with Bayesian methods.
Embedded in an extreme value approach, asymptotic normality of the estimator is
shown, and when the expert is clair-voyant, a simple combination formula can be
deduced, bridging the classical statistical approach with the expert
information. Following the aforementioned combination formula, a combination of
quantile estimators can be naturally defined. In a simulation study, the
estimator is shown to often outperform the Hill estimator for censored
observations and recent Bayesian solutions, some of which require more
information than usually available. Finally we perform a case study on a motor
third-party liability insurance claim dataset, where Hill-type and quantile
plots incorporate ultimate values into the estimation procedure in an intuitive
manner.
