Multiscale testing of qualitative hypotheses

• 成果类型: Article
• 署名作者: Dümbgen, L; Spokoiny, VG
• 署名单位: University of Lubeck; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/996986504
• 发表日期: 2001
• 页码: 124-152
• 关键词: gaussian white-noise; Nonparametric Regression; asymptotic equivalence; optimal recovery; sup-norm; multimodality; CURVES; fit

摘要

Suppose that one observes a process Y on the unit interval, where dY(t) = n(1/2)f(t) dt + dW (t) with an unknown function parameter f, given scale parameter n greater than or equal to 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.