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dc.contributor.authorFilali, Karim
dc.contributor.authorBalabdaoui, Fadoua
dc.date.accessioned2012-06-13T14:23:01Z
dc.date.available2012-06-13T14:23:01Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9451
dc.language.isoenen
dc.subjectMonte Carloen
dc.subjectMonotonicityen
dc.subjectGaver–Stehfest algorithmen
dc.subjectconcave majoranten
dc.subjectBrownian bridgeen
dc.subject.ddc519en
dc.subject.classificationjelC15en
dc.titleEfficient computation of the cdf of the maximum distance between Brownian bridge and its concave majoranten
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherYahoo! Research [Silicon Valley] http://labs.yahoo.com/Yahoo_Labs_Silicon_Valley Yahoo!;États-Unis
dc.description.abstractenIn this paper, we describe two computational methods for calculating the cumulative distribution function and the upper quantiles of the maximal difference between a Brownian bridge and its concave majorant. The first method has two different variants that are both based on a Monte Carlo approach, whereas the second uses the Gaver–Stehfest (GS) algorithm for the numerical inversion of the Laplace transform. If the former method is straightforward to implement, it is very much outperformed by the GS algorithm, which provides a very accurate approximation of the cumulative distribution as well as its upper quantiles. Our numerical work has a direct application in statistics: the maximal difference between a Brownian bridge and its concave majorant arises in connection with a nonparametric test for monotonicity of a density or regression curve on [0,1]. Our results can be used to construct very accurate rejection region for this test at a given asymptotic level.en
dc.relation.isversionofjnlnameJournal of Statistical Computation and Simulation
dc.relation.isversionofjnlvol82en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages405-418en
dc.relation.isversionofdoihttp://dx.doi.org/10.1080/00949655.2010.534481en
dc.identifier.urlsitehttp://arxiv.org/abs/1005.1307en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherTaylor & Francisen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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