The method of moments ratio estimator for the tail shape parameter. (English) Zbl 0875.62106

Danielsson, Jon; Jansen, Dennis W.; de Vries, Casper G.

Commun. Stat., Theory Methods 25, No. 4, 711-720 (1996).

Summary: The so-called Hill estimator for the shape parameter of the tail distribution is known to be downwardly biased. The Hill estimator is a moment estimator, based on the first conditional moment of the highest logarithmically transformed data. We propose a new estimator for the tail index based on the ratio of the second to the first conditional moment. This estimator has a smaller bias than the Hill estimator. We provide simulation results that demonstrate a sizable reduction in bias when \(\alpha\) is large, while the MSE is moderated as well. The new estimator is applied to stock return data in order to resolve a long standing issue in economics.

MSC:

62F10

Point estimation

Keywords:

Hill estimator; method of moments; bias

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