Multiscale testing of qualitative hypotheses

Lutz Dümbgen and Vladimir G. Spokoiny

No 1999,99, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Suppose that one observes a process Y on the unit interval, where dY(t) = n 1/ 2f(t)dt + dW(t) with an unknown function parameter f, given scale parameter n 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.

Keywords: adaptivity; concavity; Lévy's modulus of continuity; monotonicity; multiple test; nonparametric; positivity (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:199999

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