Open Access
April 2002 Risk bounds in isotonic regression
Cun-Hui Zhang
Ann. Statist. 30(2): 528-555 (April 2002). DOI: 10.1214/aos/1021379864


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.


Download Citation

Cun-Hui Zhang. "Risk bounds in isotonic regression." Ann. Statist. 30 (2) 528 - 555, April 2002.


Published: April 2002
First available in Project Euclid: 14 May 2002

zbMATH: 1012.62045
MathSciNet: MR1902898
Digital Object Identifier: 10.1214/aos/1021379864

Primary: 62G05 , 62G08
Secondary: 62G20 , 62J02

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

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 2 • April 2002
Back to Top