Multiscale Testing of Qualitative Hypotheses
Suppose that one observes a process Y on the unit interval, where dY(t) = n1/2f(t) dt + dW(t) with an unknown function parameter f, given scale parameter n ≥ 1 ("sample size") and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f su...
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| Veröffentlicht in: | The Annals of statistics 2001-02, Vol.29 (1), p.124-152 |
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| container_title | The Annals of statistics |
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| creator | Dumbgen, Lutz Spokoiny, Vladimir G. |
| description | Suppose that one observes a process Y on the unit interval, where dY(t) = n1/2f(t) dt + dW(t) with an unknown function parameter f, given scale parameter n ≥ 1 ("sample size") and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity. These tests are asymptotically optimal and adaptive in a certain sense. They are constructed via a new class of multiscale statistics and an extension of Levy's modulus of continuity of Brownian motion. |
| doi_str_mv | 10.1214/aos/996986504 |
| format | Article |
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| source | Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 62G10 62G20 adaptivity concavity Estimators Exact sciences and technology Gaussian distributions Linear regression Lévy's modulus of continuity Mathematical independent variables Mathematics monotonicity multiple test Musical intervals nonparametric Nonparametric inference Nonparametric Testing Null hypothesis positivity Probability and statistics Random variables Sciences and techniques of general use Signal bandwidth Statistical theories Statistics White noise |
| title | Multiscale Testing of Qualitative Hypotheses |
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