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


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.


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

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

Primary: 62G05
Secondary: 62E20 , 62J02

Keywords: estimation of the shape of a function , isotonic and concave regression , Nonparametric regression , simple qualitative curve characteristics

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 2 • June, 1991
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