The Annals of Statistics

Risk bounds in isotonic regression

Cun-Hui Zhang

Full-text: Open access

Abstract

Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform $n^{-1/3}$-consistency of the $\ell_p$ risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.

Article information

Source
Ann. Statist., Volume 30, Number 2 (2002), 528-555.

Dates
First available in Project Euclid: 14 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1021379864

Digital Object Identifier
doi:10.1214/aos/1021379864

Mathematical Reviews number (MathSciNet)
MR1902898

Zentralblatt MATH identifier
1012.62045

Subjects
Primary: 62G08: Nonparametric regression 62G05: Estimation
Secondary: 62J02: General nonlinear regression 62G20: Asymptotic properties

Keywords
Nonparametric regression isotonic regression risk bounds least squares estimator maximum likelihood estimator

Citation

Zhang, Cun-Hui. Risk bounds in isotonic regression. Ann. Statist. 30 (2002), no. 2, 528--555. doi:10.1214/aos/1021379864. https://projecteuclid.org/euclid.aos/1021379864


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