Open Access
February 2001 Multiscale Testing of Qualitative Hypotheses
Lutz Dümbgen, Vladimir G. Spokoiny
Ann. Statist. 29(1): 124-152 (February 2001). DOI: 10.1214/aos/996986504


Suppose that one observes a process Y on the unit interval, where dY(t) =n1/2 f(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 Lévy's modulus of continuity of Brownian motion.


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Lutz Dümbgen. Vladimir G. Spokoiny. "Multiscale Testing of Qualitative Hypotheses." Ann. Statist. 29 (1) 124 - 152, February 2001.


Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62070
MathSciNet: MR1833961
Digital Object Identifier: 10.1214/aos/996986504

Primary: 62G10
Secondary: 62G20

Keywords: Adaptivity , concavity , Lévy's modulus of continuity , Monotonicity , multiple test , nonparametric , positivity

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 1 • February 2001
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