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June 2008 Adaptive goodness-of-fit tests based on signed ranks
Angelika Rohde
Ann. Statist. 36(3): 1346-1374 (June 2008). DOI: 10.1214/009053607000000992

Abstract

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.

Citation

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Angelika Rohde. "Adaptive goodness-of-fit tests based on signed ranks." Ann. Statist. 36 (3) 1346 - 1374, June 2008. https://doi.org/10.1214/009053607000000992

Information

Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1216.62069
MathSciNet: MR2418660
Digital Object Identifier: 10.1214/009053607000000992

Subjects:
Primary: 62G10 , 62G20 , 62G35

Keywords: Exact multiple testing , Exponential inequality , multiscale statistic , relative asymptotic efficiency , sharp asymptotic adaptivity , signed ranks

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • June 2008
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