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Minimum Variance Unbiased Maximum Likelihood Estimation of the Extreme Value Index

Author

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  • 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.

Suggested Citation

  • Roger Gay, 2005. "Minimum Variance Unbiased Maximum Likelihood Estimation of the Extreme Value Index," Monash Econometrics and Business Statistics Working Papers 8/05, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2005-8
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp8-05.pdf
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    More about this item

    Keywords

    Tail-index; Minimum variance unbiased; Maximum likelihood; Asymptotically normal;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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