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What is Learnable in Valiant's Theory of the Learnable? 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Weighted least squares estimators for the Parzen tail index
Amenah AL-Najafi, László Viharos · 2020-02-28 · via math.ST updates on arXiv.org

Estimation of the tail index of heavy-tailed distributions and its applications are essential in many research areas. We propose a class of weighted least squares (WLS) estimators for the Parzen tail index. Our approach is based on the method developed by \cite{Holan2010}. We investigate consistency and asymptotic normality of the WLS estimators. Through a simulation study, we make a comparison with the Hill, Pickands, DEdH (Dekkers, Einmahl and de Haan) and ordinary least squares (OLS) estimators using the mean square error as criterion. The results show that in a restricted model some members of the WLS estimators are competitive with the Pickands, DEdH and OLS estimators.

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