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Convergence rates for smooth k-means change-point detection

Abstract : In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a k-means method. We prove that, up to a logarithmic term, this change-point estimator has a minimax rate of convergence. Then, considering the case of sparse data, with a Sobolev regularity, we propose a smoothing procedure based on Lepski's method and show that the resulting estimator attains the optimal rate of convergence. Our results are illustrated by some simulations. As the theoretical statement relying on Lepski's method depends on some unknown constant, practical strategies are suggested to perform an optimal smoothing.
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https://hal.archives-ouvertes.fr/hal-01712690
Contributor : Aurélie Fischer <>
Submitted on : Tuesday, February 20, 2018 - 2:13:30 PM
Last modification on : Friday, April 10, 2020 - 5:26:47 PM
Document(s) archivé(s) le : Sunday, May 6, 2018 - 6:55:20 AM

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  • HAL Id : hal-01712690, version 1
  • ARXIV : 1802.07617

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Aurélie Fischer, Dominique Picard. Convergence rates for smooth k-means change-point detection. 2018. ⟨hal-01712690⟩

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