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.
Publié le : 1991-06-14
Classification:
Nonparametric regression,
simple qualitative curve characteristics,
isotonic and concave regression,
estimation of the shape of a function,
62G05,
62J02,
62E20
@article{1176348118,
author = {Mammen, Enno},
title = {Nonparametric Regression Under Qualitative Smoothness Assumptions},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 741-759},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348118}
}
Mammen, Enno. Nonparametric Regression Under Qualitative Smoothness Assumptions. Ann. Statist., Tome 19 (1991) no. 1, pp. 741-759. http://gdmltest.u-ga.fr/item/1176348118/