Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions
标量遍历扩散过程的精确自适应与路径稳定相似性检验
Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift b to some reference drift b0: At prescribed significance, we simultaneously identify those regions where violation from similarity occurs, without a priori knowledge of their number, size and location. This test is shown to be minimax-optimal and adaptive. At the same time, the procedure is robust under small deviation from Brownian motion as the driving noise…