The method of moments ratio estimator for the tail shape parameter
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 25 (4) , 711-720
- https://doi.org/10.1080/03610929608831727
Abstract
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 a 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.Keywords
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