Institute of Mathematical Statistics Lecture Notes - Monograph Series

Additive isotone regression

Enno Mammen and Kyusang Yu

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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

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

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

isotone regression additive regression oracle property pool adjacent violator algorithm backfitting

Copyright © 2007, Institute of Mathematical Statistics


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.

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