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A shift and scale invariant estimator for index of extreme value distribution

In many fields in the world of finance and insurance extreme events tend to occur more frequently than one would expect under classical statistical assumptions. The random mechanisms generating these events are called heavy tailed, indicating that the underlying probability distributions have tails that decay essentially as power functions. In the analysis of such heavy tailed data and in the estimation of extreme quantiles and tail probabilities the extreme value index plays a decisive role. In this paper, we are interested in overviews of the main methods on tail index estimation and outline a shift and scale invariant estimator, which is much simpler to use in practice. We next proceed to an asymptotic comparison of these estimators at their optimal levels. An illustration of the finite sample behavior of the estimators is provided through representative procedures.