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VOL. 55 | 2007 Additive isotone regression
Enno Mammen, Kyusang Yu

Editor(s) Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner

IMS Lecture Notes Monogr. Ser., 2007: 179-195 (2007) DOI: 10.1214/074921707000000355


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.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

zbMATH: 1176.62035
MathSciNet: MR2459939

Digital Object Identifier: 10.1214/074921707000000355

Primary: 62G07 , 62G20

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

Rights: Copyright © 2007, Institute of Mathematical Statistics


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