Minimum Variance Unbiased Maximum Likelihood Estimation of the Extreme Value Index

Roger Gay ()

No 8/05, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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.

Keywords: Tail-index; Minimum variance unbiased; Maximum likelihood; Asymptotically normal (search for similar items in EconPapers)
JEL-codes: C13 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2005-04
New Economics Papers: this item is included in nep-ecm and nep-rmg
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