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Multiscale testing of qualitative hypotheses

Author

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  • Dümbgen, Lutz
  • Spokoiny, Vladimir G.

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.

Suggested Citation

  • Dümbgen, Lutz & Spokoiny, Vladimir G., 1999. "Multiscale testing of qualitative hypotheses," SFB 373 Discussion Papers 1999,99, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199999
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