The extreme value theory is very popular in applied sciences includingFinance, economics, hydrology and many other disciplines. In univariate extremevalue theory, we model the data by a suitable distribution from the generalmax-domain of attraction (MAD) characterized by its tail index; there are threebroad classes of tails -- the Pareto type, the Weibull type and the Gumbeltype. The simplest and most common estimator of the tail index is the Hillestimator that works only for Pareto type tails and has a high bias; it is alsohighly non-robust in presence of outliers with respect to the assumed model.There have been some recent attempts to produce asymptotically unbiased orrobust alternative to the Hill estimator; however all the robust alternativeswork for any one type of tail. This paper proposes a new general estimator ofthe tail index that is both robust and has smaller bias under all the threetail types compared to the existing robust estimators. This essentiallyproduces a robust generalization of the estimator proposed by Matthys andBeirlant (2003) under the same model approximation through a suitableexponential regression framework using the density power divergence. Therobustness properties of the estimator are derived in the paper along with anextensive simulation study. A method for bias correction is also proposed withapplication to some real data examples.
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