At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics
Donsker 定理的边界:多尺度扫描统计量的渐近理论
For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values strongly depend on the noise distribution, and we argue that existing methods are either statistically infeasible, or asymptotically sub-optimal. To address this methodological challenge, we show how to develop a feasible multiscale test via…