Multiscale Testing of Qualitative Hypotheses
نویسنده
چکیده
Suppose that one observes a process Y on the unit interval, where dY t = n1/2f 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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