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Ratio of Generalized Hill’s estimator and its asymptotic normality theory

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Ratio of Generalized Hill’s estimator and its asymptotic normality theory

Content Provider	Springer Nature Link
Author	Diop, A. Lô, G. S.
Copyright Year	2009
Abstract	We present a statistical process depending on a continuous time parameter τ whose each margin provides a Generalized Hill’s estimator. In this paper, the asymptotic normality of the finite-dimensional distributions of this family are completely characterized for τ > 1/2 when the underlying distribution function lies on the maximum domain of attraction. The ratio of two different margins of the statistical process characterizes entirely the whole domain of attraction. Its asymptotic normality is also studied. The results permit in general to build a new family of estimators for the extreme value index whose asymptotic properties can be easily derived. For example, we give a new estimate of the Weibull extreme value index and we study its consistency and its asymptotic normality.
Starting Page	117
Ending Page	133
Page Count	17
File Format	PDF
ISSN	10665307
Journal	Mathematical Methods of Statistics
Volume Number	18
Issue Number	2
e-ISSN	19348045
Language	English
Publisher	Allerton Press, Inc.
Publisher Date	2009-07-01
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	order statistics empirical and quantile processes Brownian bridges maximum domain of attraction asymptotic normality extreme value theory Statistics of extreme values; tail inference Order statistics; empirical distribution functions Asymptotic properties of estimators Statistical Theory and Methods
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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Ratio of Generalized Hill’s estimator and its asymptotic normality theory

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