Adaptive goodness-of-fit tests based on signed ranks

Details Adaptive goodness-of-fit tests based on signed ranks Adaptive goodness-of-fit tests based on signed ranks

2008-06-18

arxiv.org/abs/0806.2985v1

Annals of Statistics 2008, Vol. 36, No. 3, 1346-1374

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000992 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000992

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 H\"{o}lder 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 H\"{o}lder classes simultaneously.

Affiliated with

Also associated with

No associations

Rating

Adaptive goodness-of-fit tests based on signed ranks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Adaptive goodness-of-fit tests based on signed ranks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adaptive goodness-of-fit tests based on signed ranks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-272880