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2020 Estimating piecewise monotone signals
Kentaro Minami
Electron. J. Statist. 14(1): 1508-1576 (2020). DOI: 10.1214/20-EJS1700


We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the nearly-isotonic regression proposed by Tibshirani et al. (2011). We derive risk bounds for the nearly-isotonic regression estimators that are adaptive to piecewise monotone signals. The estimator achieves a near minimax convergence rate over certain classes of piecewise monotone signals under a weak assumption. Furthermore, we present an algorithm that can be applied to the nearly-isotonic type estimators on general weighted graphs. The simulation results suggest that the nearly-isotonic regression performs as well as the ideal estimator that knows the true positions of changepoints.


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Kentaro Minami. "Estimating piecewise monotone signals." Electron. J. Statist. 14 (1) 1508 - 1576, 2020.


Received: 1 May 2019; Published: 2020
First available in Project Euclid: 9 April 2020

zbMATH: 07200236
MathSciNet: MR4082476
Digital Object Identifier: 10.1214/20-EJS1700

Keywords: adaptive risk bounds , isotonic regression , nearly-isotonic regression , Piecewise monotone function


Vol.14 • No. 1 • 2020
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