Abstract
Abstract The main goal of this paper is to present generalized Hill estimators parametrized in a positive real α (and equal to the Hill estimator when α =1), which are asymptotically more efficient than the Hill estimator for a large region of values of α for any point of the ( γ , ρ )-plane, where γ >0 is the tail index , related to the heaviness of the tail 1− F of the underlying model F , and ρ ⩽0 is the second-order parameter , related to the rate of convergence of maximum values, linearly normalized, towards its limit. The practical validation of asymptotic results for small finite samples is done by means of simulation techniques in Frechet and Burr models, and some indications are provided on the choice of α .
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