Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910411251515392 |
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| author | Brutsche, Johannes Rohde, Angelika |
| author_facet | Brutsche, Johannes Rohde, Angelika |
| contents | Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift $b$ to some reference drift $b_0$: At prescribed significance, we simultaneously identify those regions where violation from similiarity 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_13776 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions Brutsche, Johannes Rohde, Angelika Statistics Theory Probability Methodology Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift $b$ to some reference drift $b_0$: At prescribed significance, we simultaneously identify those regions where violation from similiarity 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. |
| title | Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions |
| topic | Statistics Theory Probability Methodology |
| url | https://arxiv.org/abs/2203.13776 |