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A heuristic choice of tuning parameters in a location invariant reduced-bias estimation of the extreme value index: Application to financial log-returns and simulated data

In this paper, we provide a simple heuristic choice of the tuning parameters involved in a location and scale invariant semi-parametric estimation of a positive extreme value index (EV I), the primary parameter in Statistics of Extremes. Under such a context of heavy-tailed underlying parents, the classical EVI-estimators are Hill estimators, based on any intermediate number k of top order statistics. But these EVI estimators are not location-invariant, contrarily to the PORT-Hill estimators, which depend on an extra tuning parameter q, with 0 ≤ q < 1. On the basis of second-order minimum-variance reduced-bias (MV RB) EVI-estimators, we shall here consider PORT-MVRB EVI-estimators, and propose a heuristic procedure for the adaptive choice of k and q. Applications in the field of finance and to simulated data are provided.