Multiscale Change-point Segmentation: Beyond Step Functions

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​Multiscale Change-point Segmentation: Beyond Step Functions​
Li, H. ; Guo, Q. & Munk, A. ​ (2019) 
Electronic Journal of Statistics13(2) pp. 3254​-3296​.​

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Authors
Li, Housen 
Guo, Qinghai
Munk, Axel 
Abstract
Modern multiscale type segmentation methods are known to detect multiple change-points with hii gh statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models which assume the signal as an unkk nown piecewise constant function. In this paper this will be extended to certain function classes beyond step functions in a nonparametric regression see tting, revealing certain multiscale segmentation methods as robust to deviation from such piecewise constant functions. Although these methods are desigg ned for step functions, our main finding is its adaptation over such function classes for a universal thresholding. On the one hand, this includes nearll y optimal convergence rates for step functions with increasing number of jumps. On the other hand, for models which are characterized by certain approxii mation spaces, we obtain nearly optimal rates as well. This includes bounded variation functions, and (piecewise) Hölder functions of smoothness orr der 0<α≤1. All results are formulated in terms of Lp-loss (0<p<∞) both almost surely and in expectation. Theoretical findings are examined by various nuu merical simulations.
Issue Date
2019
Type
Journal Article
Subtype
original_ja
Journal
Electronic Journal of Statistics 
Project
RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems 
EXC 2067: Multiscale Bioimaging 
Working Group
RG Li 
RG Munk 
Language
English

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