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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2007, Number 1, Pages 3–24
(Mi basm46)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/basm46 https://www.mathnet.ru/eng/basm/y2007/i1/p3
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Abstract page: | 549 | Full-text PDF : | 115 | References: | 55 |
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