Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2007, Number 1, Pages 3–24 (Mi basm46)  
This article is cited in 3 scientific papers (total in 3 papers)

Pareto approximation of the tail by local exponential modeling

Ion Gramaa, Vladimir Spokoinyb

a Université de Bretagne Sud, Tohannic, Vannes, France
b Weierstrass Institute, Berlin, Germany
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Abstract: We give a new adaptive method for selecting the number of upper order statistics used in the estimation of the tail of a distribution function. Our approach is based on approximation by an exponential model. The selection procedure consists in consecutive testing for the hypothesis of homogeneity of the estimated parameter against the change-point alternative. The selected number of upper order statistics corresponds to the first detected change-point. Our main results are non-asymptotic.
Keywords and phrases: nonparametric adaptive estimation, extreme values, tail index, Hill estimator, probabilities of rare events.
Received: 12.07.2006
Bibliographic databases:
MSC: Primary 62G32, 62G08; Secondary 62G05
Language: English
Citation: Ion Grama, Vladimir Spokoiny, “Pareto approximation of the tail by local exponential modeling”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, no. 1, 3–24
Citation in format AMSBIB
\Bibitem{GraSpo07}
\by Ion~Grama, Vladimir~Spokoiny
\paper Pareto approximation of the tail by local exponential modeling
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2007
\issue 1
\pages 3--24
\mathnet{http://mi.mathnet.ru/basm46}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2324403}
\zmath{https://zbmath.org/?q=an:1122.62035}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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