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  Multiscale change-point segmentation: beyond step functions.

Li, H., Guo, Q., & Munk, A. (2019). Multiscale change-point segmentation: beyond step functions. Electronic Journal of Statistics, 13(2), 3254-3296. doi:10.1214/19-EJS1608.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-867A-B Version Permalink: http://hdl.handle.net/21.11116/0000-0005-867D-8
Genre: Journal Article

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 Creators:
Li, H., Author
Guo, Q., Author
Munk, A.1, Author              
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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Free keywords: Change-point regression; adaptive estimation; oracle inequality; jump detection; model misspecification; multiscale inference; approximation spaces; robustness
 Abstract: Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning (minimax) estimation theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper, for a large collection of multiscale segmentation methods (including various existing procedures), such theory will be extended to certain function classes beyond step functions in a nonparametric regression setting. This extends the interpretation of such methods on the one hand and on the other hand reveals these methods as robust to deviation from piecewise constant functions. Our main finding is the adaptation over nonlinear approximation classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Holder functions of smoothness order 0 < alpha <= 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a log-factor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations.

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Language(s): eng - English
 Dates: 2019-09-25
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1214/19-EJS1608
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Title: Electronic Journal of Statistics
Source Genre: Journal
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Pages: - Volume / Issue: 13 (2) Sequence Number: - Start / End Page: 3254 - 3296 Identifier: -