# Template Matching and Change Point Detection by M-estimation

arXiv: https://arxiv.org/abs/2009.04072 · HTML: https://mlsanity.com/paper/2009.04072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [Widely Linear Matched Filter: A Lynchpin towards the Interpretability of Complex-valued CNNs](https://mlsanity.com/paper/2401.16729/) (2024)

## Abstract (arXiv)

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.