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2020 The bias of isotonic regression
Ran Dai, Hyebin Song, Rina Foygel Barber, Garvesh Raskutti
Electron. J. Statist. 14(1): 801-834 (2020). DOI: 10.1214/20-EJS1677

Abstract

We study the bias of the isotonic regression estimator. While there is extensive work characterizing the mean squared error of the isotonic regression estimator, relatively little is known about the bias. In this paper, we provide a sharp characterization, proving that the bias scales as $O(n^{-\beta /3})$ up to log factors, where $1\leq \beta \leq 2$ is the exponent corresponding to Hölder smoothness of the underlying mean. Importantly, this result only requires a strictly monotone mean and that the noise distribution has subexponential tails, without relying on symmetric noise or other restrictive assumptions.

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Ran Dai. Hyebin Song. Rina Foygel Barber. Garvesh Raskutti. "The bias of isotonic regression." Electron. J. Statist. 14 (1) 801 - 834, 2020. https://doi.org/10.1214/20-EJS1677

Information

Received: 1 August 2019; Published: 2020
First available in Project Euclid: 5 February 2020

zbMATH: 07163274
MathSciNet: MR4059933
Digital Object Identifier: 10.1214/20-EJS1677

Subjects:
Primary: 62G08

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Vol.14 • No. 1 • 2020
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