摘要：Bias reduction in tail estimation has received considerable interest in extreme value
analysis. Estimation methods that minimize the bias while keeping the mean squared
error (MSE) under control, are especially useful when applying classical methods such
as the Hill (1975) estimator. In the case of heavy tailed distributions, Caeiro et al.
(2005) proposed minimum variance reduced bias estimators of the extreme value index,
where the bias is reduced without increasing the variance with respect to the
Hill estimator. This method is based on adequate external estimation of a pair of
parameters of second order slow variation under a third order condition. Here we
revisit this problem exploiting the mathematical fact that the bias tends to 0 with
increasing threshold. This leads to shrinkage estimation for the extreme value index,
which allows for a penalized likelihood and a Bayesian implementation. This new
approach is applied starting from the approximation to excesses over a high threshold
using the extended Pareto distribution, as developed in Beirlant et al. (2009).
We present asymptotic results for the resulting shrinkage penalized likelihood estimator
of the extreme value index. Finite sample simulation results are proposed both
for the penalized likelihood and Bayesian implementation. We then compare with the
minimum variance reduced bias estimators.
关键词：extreme value index; tail estimation; extended Pareto distribution; shrinkage estimators;
