Additive isotone regression. (English) Zbl 1176.62035

Mammen, Enno; Yu, Kyusang

Cator, Eric A. (ed.) et al., Asymptotics: particles, processes and inverse problems. Festschrift for Piet Groeneboom. Papers based on the presentations at the workshop, Delft, The Netherland, July 10–14, 2006. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-71-3/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 55, 179-195 (2007).

Summary: This paper is about optimal estimation of the additive components of a nonparametric, additive isotonic 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.
For the entire collection see [Zbl 1165.60002].

MSC:

62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference
65C60	Computational problems in statistics (MSC2010)

Keywords:

additive regression; oracle property; pool adjacent violator algorithm; backfitting; simulations