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Minimum Variance Unbiased Maximum Likelihood Estimation of the Extreme Value Index

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Author Info
Roger Gay ()
Abstract

New results for ratios of extremes from distributions with a regularly varying tail are presented. Deriving from independence results for certain functions of order statistics, 'consecutive' ratios of extremes are shown to be independent as well as non-distribution specific. They have tractable distributions related to beta distributions. The minimum variance unbiased maximum likelihood estimator has the form of Hill's estimator. It achieves the Cramer-Rao minimum variance bound and is a function of a sufficient statistic. For small sample sizes the form of the moment generating function of the estimator shows it has a gamma distribution.

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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2005/wp8-05.pdf
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Publisher Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 8/05.

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Length: 11 pages
Date of creation: Apr 2005
Date of revision:
Handle: RePEc:msh:ebswps:2005-8

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Related research
Keywords: Tail-index; Minimum variance unbiased; Maximum likelihood; Asymptotically normal;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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This page was last updated on 2009-10-21.

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