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.
Publié le : 2001-02-14
Classification:
adaptivity,
concavity,
Lévy's modulus of continuity,
monotonicity,
multiple test,
nonparametric,
positivity,
62G10,
62G20
@article{996986504,
author = {D\"umbgen, Lutz and Spokoiny, Vladimir G.},
title = {Multiscale Testing of Qualitative Hypotheses},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 124-152},
language = {en},
url = {http://dml.mathdoc.fr/item/996986504}
}
Dümbgen, Lutz; Spokoiny, Vladimir G. Multiscale Testing of Qualitative Hypotheses. Ann. Statist., Tome 29 (2001) no. 2, pp. 124-152. http://gdmltest.u-ga.fr/item/996986504/