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Localising change points in piecewise polynomials of general degrees
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Yu, Yi, Chatterjee, Sabyasachi and Xu, Haotian (2022) Localising change points in piecewise polynomials of general degrees. Electronic Journal of Statistics, 16 (1). pp. 1855-1890. doi:10.1214/21-EJS1963 ISSN 1935-7524.
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Official URL: https://doi.org/10.1214/21-EJS1963
Abstract
In this paper we are concerned with a sequence of univariate random variables with piecewise polynomial means and independent sub-Gaussian noise. The underlying polynomials are allowed to be of arbitrary but fixed degrees. All the other model parameters are allowed to vary depending on the sample size.
We propose a two-step estimation procedure based on the ℓ0-penalisation and provide upper bounds on the localisation error. We complement these results by deriving global information-theoretic lower bounds, which show that our two-step estimators are nearly minimax rate-optimal. We also show that our estimator enjoys near optimally adaptive performance by attaining individual localisation errors depending on the level of smoothness at individual change points of the underlying signal. In addition, under a special smoothness constraint, we provide a minimax lower bound on the localisation errors. This lower bound is independent of the polynomial orders and is sharper than the global minimax lower bound.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Polynomials , Stochastic analysis , Nonparametric statistics | ||||||
| Journal or Publication Title: | Electronic Journal of Statistics | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1935-7524 | ||||||
| Official Date: | 21 March 2022 | ||||||
| Dates: |
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| Volume: | 16 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 1855-1890 | ||||||
| DOI: | 10.1214/21-EJS1963 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 4 October 2022 | ||||||
| Date of first compliant Open Access: | 4 October 2022 | ||||||
| RIOXX Funder/Project Grant: |
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