Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/61743
Authors: 
Dümbgen, Lutz
Spokoiny, Vladimir G.
Year of Publication: 
1999
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,99
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.
Subjects: 
adaptivity
concavity
Lévy's modulus of continuity
monotonicity
multiple test
nonparametric
positivity
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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