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2019 Contraction and uniform convergence of isotonic regression
Fan Yang, Rina Foygel Barber
Electron. J. Statist. 13(1): 646-677 (2019). DOI: 10.1214/18-EJS1520

Abstract

We consider the problem of isotonic regression, where the underlying signal $x$ is assumed to satisfy a monotonicity constraint, that is, $x$ lies in the cone $\{x\in \mathbb{R}^{n}:x_{1}\leq \dots\leq x_{n}\}$. We study the isotonic projection operator (projection to this cone), and find a necessary and sufficient condition characterizing all norms with respect to which this projection is contractive. This enables a simple and non-asymptotic analysis of the convergence properties of isotonic regression, yielding uniform confidence bands that adapt to the local Lipschitz properties of the signal.

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Fan Yang. Rina Foygel Barber. "Contraction and uniform convergence of isotonic regression." Electron. J. Statist. 13 (1) 646 - 677, 2019. https://doi.org/10.1214/18-EJS1520

Information

Received: 1 April 2018; Published: 2019
First available in Project Euclid: 16 February 2019

zbMATH: 07038000
MathSciNet: MR3914177
Digital Object Identifier: 10.1214/18-EJS1520

Subjects:
Primary: 62G07, 62G08

JOURNAL ARTICLE
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Vol.13 • No. 1 • 2019
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