## Electronic Journal of Statistics

### The bias of isotonic regression

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 14, Number 1 (2020), 801-834.

Dates
First available in Project Euclid: 5 February 2020

https://projecteuclid.org/euclid.ejs/1580871776

Digital Object Identifier
doi:10.1214/20-EJS1677

Mathematical Reviews number (MathSciNet)
MR4059933

Zentralblatt MATH identifier
07163274

Subjects
Primary: 62G08: Nonparametric regression

Keywords
Isotonic regression bias

#### Citation

Dai, Ran; Song, Hyebin; Barber, Rina Foygel; Raskutti, Garvesh. The bias of isotonic regression. Electron. J. Statist. 14 (2020), no. 1, 801--834. doi:10.1214/20-EJS1677. https://projecteuclid.org/euclid.ejs/1580871776

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