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- W3104395848 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." @default.
- W3104395848 created "2020-11-23" @default.
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- W3104395848 date "2008-06-01" @default.
- W3104395848 modified "2023-09-27" @default.
- W3104395848 title "Adaptive goodness-of-fit tests based on signed ranks" @default.
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- W3104395848 doi "https://doi.org/10.1214/009053607000000992" @default.
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