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

Abstract

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.

Citation

Download Citation

Kentaro Minami. "Estimating piecewise monotone signals." Electron. J. Statist. 14 (1) 1508 - 1576, 2020. https://doi.org/10.1214/20-EJS1700

Information

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

JOURNAL ARTICLE
69 PAGES


SHARE
Vol.14 • No. 1 • 2020
Back to Top