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June, 1991 Nonparametric Regression Under Qualitative Smoothness Assumptions
Enno Mammen
Ann. Statist. 19(2): 741-759 (June, 1991). DOI: 10.1214/aos/1176348118

Abstract

We propose a new nonparametric regression estimate. In contrast to the traditional approach of considering regression functions whose $m$th derivatives lie in a ball in the $L_\infty$ or $L_2$ norm, we consider the class of functions whose $(m - 1)$st derivative consists of at most $k$ monotone pieces. For many applications this class seems more natural than the classical ones. The least squares estimator of this class is studied. It is shown that the speed of convergence is as fast as in the classical case.

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Enno Mammen. "Nonparametric Regression Under Qualitative Smoothness Assumptions." Ann. Statist. 19 (2) 741 - 759, June, 1991. https://doi.org/10.1214/aos/1176348118

Information

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

zbMATH: 0737.62039
MathSciNet: MR1105842
Digital Object Identifier: 10.1214/aos/1176348118

Subjects:
Primary: 62G05
Secondary: 62E20, 62J02

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 2 • June, 1991
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