Template Matching with Ranks
Ery Arias-Castro, Lin Zheng

TL;DR
This paper introduces a rank-based template matching method for noisy signals, demonstrating its asymptotic normality and parametric convergence rate through theoretical analysis and numerical simulations.
Contribution
It proposes a novel rank-based estimator for template matching that achieves optimal asymptotic properties, extending existing signal processing techniques.
Findings
Estimator achieves parametric rate of convergence
Estimator is asymptotically normal
Numerical simulations support theoretical results
Abstract
We consider the problem of matching a template to a noisy signal. Motivated by some recent proposals in the signal processing literature, we suggest a rank-based method and study its asymptotic properties using some well-established techniques in empirical process theory combined with H\'ajek's projection method. The resulting estimator of the shift is shown to achieve a parametric rate of convergence and to be asymptotically normal. Some numerical simulations corroborate these findings.
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Taxonomy
TopicsControl Systems and Identification · Blind Source Separation Techniques · Statistical Methods and Inference
