Template Matching and Change Point Detection by M-Estimation
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive the convergence rate and the asymptotic distribution of the...
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| Veröffentlicht in: | IEEE transactions on information theory 2022-01, Vol.68 (1), p.423-447 |
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| creator | Arias-Castro, Ery Zheng, Lin |
| description | We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive the convergence rate and the asymptotic distribution of the M-estimator under relatively mild assumptions. We also discuss the optimality of the estimator, both in finite samples in the minimax sense and in the large-sample limit in terms of local minimaxity and relative efficiency. Although most of the paper is dedicated to the study of the basic shift model in the context of a random design, we consider many extensions towards the end of the paper, including more flexible templates, fixed designs, the agnostic setting, and more. |
| doi_str_mv | 10.1109/TIT.2021.3112680 |
| format | Article |
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| source | IEEE Electronic Library (IEL) |
| subjects | change point detection Convergence empirical processes M-estimation Matched filter Maximum likelihood estimation minimax optimality Minimax technique Noise measurement scan statistics Shape signal alignment Signal processing Task analysis Template matching |
| title | Template Matching and Change Point Detection by M-Estimation |
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