Template Matching and Change Point Detection by M-Estimation
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Publication:5030297
DOI10.1109/TIT.2021.3112680zbMATH Open1489.94024arXiv2009.04072OpenAlexW3199701497MaRDI QIDQ5030297
Publication date: 17 February 2022
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/2009.04072
Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Detection theory in information and communication theory (94A13)
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