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June, 1991 Estimating a Smooth Monotone Regression Function
Enno Mammen
Ann. Statist. 19(2): 724-740 (June, 1991). DOI: 10.1214/aos/1176348117


The problem of estimating a smooth monotone regression function $m$ will be studied. We will consider the estimator $m_{SI}$ consisting of a smoothing step (application of a kernel estimator based on a kernel $K$) and of a isotonisation step (application of the pool adjacent violator algorithm). The estimator $m_{SI}$ will be compared with the estimator $m_{IS}$ where these two steps are interchanged. A higher order stochastic expansion of these estimators will be given which show that $m_{SI}$ and $m_{SI}$ are asymptotically first order equivalent and that $m_{IS}$ has a smaller mean squared error than $m_{SI}$ if and only if the kernel function of the kernel estimator is not too smooth.


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Enno Mammen. "Estimating a Smooth Monotone Regression Function." Ann. Statist. 19 (2) 724 - 740, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0737.62038
MathSciNet: MR1105841
Digital Object Identifier: 10.1214/aos/1176348117

Primary: 62G05
Secondary: 62E20 , 62J02

Keywords: isotonic regression , Kernel estimator , Nonparametric regression

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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