Abstract
The Hill's estimator (Hill, 1975) has been largely used in extreme value theory in order to estimate the tail index associated to a distribution function with a positive index. One of the criticisms to its use is the possible associated bias, dependent on the top portion of the original sample used, and also the fact that it is not location invariant. Here, a new Hill-type estimator is studied, which is location invariant. This new estimator is based on the original Hill's estimator, but is made location invariant by a random shift. Its asymptotic distributional behavior is derived, in a semiparametric setup. A comparative simulation study is also presented for several models, following an appropriate adaptive procedure.
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Fraga Alves, M. A Location Invariant Hill-Type Estimator. Extremes 4, 199–217 (2001). https://doi.org/10.1023/A:1015226104400
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DOI: https://doi.org/10.1023/A:1015226104400