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

62F10 Point estimation
Full Text: DOI
[1] Danielsson J., Mimeo (1994)
[2] DOI: 10.1093/qmath/38.1.45 · Zbl 0611.26001 · doi:10.1093/qmath/38.1.45
[3] DOI: 10.1214/aos/1176346723 · Zbl 0539.62048 · doi:10.1214/aos/1176346723
[4] Hall Peter, J. Roy. Statis. Soc. B 44 pp 37– (1982)
[5] Haan De L., mimeo (1994)
[6] DOI: 10.1214/aos/1176343247 · Zbl 0323.62033 · doi:10.1214/aos/1176343247
[7] DOI: 10.2307/2109682 · doi:10.2307/2109682
[8] DOI: 10.1016/0927-5398(94)90004-3 · doi:10.1016/0927-5398(94)90004-3
[9] Schwart, G William. Business cycles, financial crises and stock volatility. Carnegie- Rochester Conference Series on Public Policy. Vol. 31, pp.83–126.
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