Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions
在非参数扩散模型中，开发了一种多重检验方法，用于推断未知漂移与参考漂移的相似性，无需先验知识即可同时识别违规区域，且该方法具有极小极大最优性和自适应性，对驱动噪声的小偏差具有稳健性。
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 process. A detailed investigation for fractional driving noise, which is neither a semimartingale nor a Markov process, is provided for Hurst indices close to the Brownian motion case.