Template Matching and Change Point Detection by M-estimation
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.
Cite
@article{arxiv.2009.04072,
title = {Template Matching and Change Point Detection by M-estimation},
author = {Ery Arias-Castro and Lin Zheng},
journal= {arXiv preprint arXiv:2009.04072},
year = {2020}
}