| Abstract: | We define the extreme values of any random sample of size nfrom a distribution function F as the observations exceedinga threshold and following a type of generalized Pareto distribution(GPD) involving the tail index of F. The threshold is the orderstatistic that minimizes a Kolmogorov-Smirnov statistic betweenthe empirical distribution of the corresponding largest observationsand the corresponding GPD. To formalize the definition we usea semiparametric bootstrap to test the corresponding GPD approximation.Finally, we use our methodology to estimate the tail index andvalue at risk (VaR) of some financial indexes of major stockmarkets. |
