摘要：TV shows on any athletic event make clear that those who want gold medals cannot
dispense statistics. And the statistics more appealing to champions and coachers are
the extreme order statistics, and in particular maximum (or minimum) values and
records. The models in statistics of extremes are usually semi-parametric or even
non-parametric in nature, with the imposition of a few regularity conditions in the
appropriate tail of the unknown model underlying the available data. The primordial
parameter is the extreme value index, the shape parameter in the (unified) extreme
value distribution. The estimation of the extreme value index is one of the basis
for the estimation of other parameters of rare events, like the right endpoint of the
model underlying the data, a high quantile, the return period and the probability of
exceedance of a high level. In this paper, we are interested in an application of statistics
of extremes to the best personal marks in a few athletic events. Due to the way data
are collected, we begin with a parametric data analysis, but we pay special attention
to the semi-parametric estimation of the extreme value index and the right endpoint
whenever finite, the possible world record, given the actual conditions. In order to
achieve a better decision we consider a few alternative semi-parametric estimators
available in the literature, and heuristic rules for the choice of thresholds.
关键词：statistics of extremes; athletics; semi-parametric estimation; extreme value index;
right endpoint; excellence indicators; Monte Carlo methodology.
