Institute of Mathematical Statistics Lecture Notes - Monograph Series

Additive isotone regression

Enno Mammen and Kyusang Yu

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Abstract

This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a least squares estimator if the other components were known. The algorithm for the calculation of the estimator uses backfitting. Convergence of the algorithm is shown. Finite sample properties are also compared through simulation experiments.

Chapter information

Source
Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner, eds., Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 179-195

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196797076

Digital Object Identifier
doi:10.1214/074921707000000355

Mathematical Reviews number (MathSciNet)
MR2459939

Zentralblatt MATH identifier
1176.62035

Subjects
Primary: 62G07: Density estimation 62G20: Asymptotic properties

Keywords
isotone regression additive regression oracle property pool adjacent violator algorithm backfitting

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

Mammen, Enno; Yu, Kyusang. Additive isotone regression. Asymptotics: Particles, Processes and Inverse Problems, 179--195, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000355. https://projecteuclid.org/euclid.lnms/1196797076


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