Reiss and Thomas automatic selection of the number of extremes ?
Most widely used semi-parametric estimators of the extreme value parameter depend on the number of upper extremes which locate where the tail of a distribution begins. In the presence of a random sample with finite size, the problem concerning the choice of the number of upper extremes is not easy to handle. This number k is not only governed by the sample size n, but also ruled by parameters characterizing F. When the underlying distribution function is known, the optimum value k can be attained through the minimization of the asymptotic mean squared error of the considered estimator. Nevertheless, the merit of such procedure may be compromised by the assessment of k values equaling the sample size n. An alternative procedure entails that the adequate number k should be the value which minimizes a mean distance encapsulating a penalty term just as presented by Reiss and Thomas (Statistical Analysis of Extreme Values, Birkhuser, Basel, 1997, P. 121). The performance evaluation of Reiss and Thomas heuristic procedure will be carried out undertaking the asymptotically determined k values as a reference.
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