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arXiv · 2009.04072

Template Matching and Change Point Detection by M-estimation

Ery Arias-Castro·Lin Zheng
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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.

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Ery Arias-Castro, Lin Zheng. 2020-09-09. Template Matching and Change Point Detection by M-estimation. https://arxiv.org/abs/2009.04072

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