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 Hájek’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.
Acknowledgements
We are very grateful to Richard Nickl and Nicolas Verzelen for helpful discussions and pointers.
Citation
Ery Arias-Castro. Lin Zheng. "Template matching with ranks." Bernoulli 29 (1) 52 - 74, February 2023. https://doi.org/10.3150/21-BEJ1449
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