Adaptive goodness-of-fit tests based on signed ranks

dc.creatorRohde, Angelika
dc.date2008-06-18
dc.date.accessioned2026-07-07T12:19:37Z
dc.date.available2026-07-07T12:19:37Z
dc.descriptionWithin the nonparametric regression model with unknown regression function $l$ and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis $l=0$ against a nonparametric alternative is proposed. This test is distribution-free and exact for finite samples even in the heteroscedastic case. It adapts in a certain sense to the unknown smoothness of the regression function under the alternative, and it is uniformly consistent against alternatives whose sup-norm tends to zero at the fastest possible rate. The test is shown to be asymptotically optimal in two senses: It is rate-optimal adaptive against Hölder classes. Furthermore, its relative asymptotic efficiency with respect to an asymptotically minimax optimal test under sup-norm loss is close to 1 in case of homoscedastic Gaussian errors within a broad range of Hölder classes simultaneously.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000992 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0806.2985
dc.identifierhttp://arxiv.org/abs/0806.2985
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 3, 1346-1374
dc.identifierdoi:10.1214/009053607000000992
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212815
dc.subjectStatistics Theory
dc.subject62G10, 62G20, 62G35 (Primary)
dc.titleAdaptive goodness-of-fit tests based on signed ranks
dc.typetext

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