Adaptive goodness-of-fit tests based on signed ranks
| dc.creator | Rohde, Angelika | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T12:19:37Z | |
| dc.date.available | 2026-07-07T12:19:37Z | |
| dc.description | Within 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.description | Published 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.identifier | https://arxiv.org/abs/0806.2985 | |
| dc.identifier | http://arxiv.org/abs/0806.2985 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 3, 1346-1374 | |
| dc.identifier | doi:10.1214/009053607000000992 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212815 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G10, 62G20, 62G35 (Primary) | |
| dc.title | Adaptive goodness-of-fit tests based on signed ranks | |
| dc.type | text |