Asymptotically unbiased estimation of the second order tail parameter

Tertius de Wet, Yuri Goegebeur and Maria Reimert Munch

Statistics & Probability Letters, 2012, vol. 82, issue 3, 565-573

Abstract: We introduce a class of asymptotically unbiased estimators for the second order parameter in extreme value statistics. The estimators are constructed by means of an appropriately chosen linear combination of two simple, but biased, kernel estimators for the second order parameter. Asymptotic normality is proven under a third order condition on the tail behavior, some conditions on the kernel functions and for an intermediate number of upper order statistics. A specific member from the proposed class, obtained with power kernel functions, is derived and its finite sample behavior studied in a small simulation experiment.

Keywords: Pareto-type distribution; Second order parameter; Third order condition; Bias correction (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.11.016

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