The Annals of Statistics
- Ann. Statist.
- Volume 19, Number 2 (1991), 741-759.
Nonparametric Regression Under Qualitative Smoothness Assumptions
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.
Ann. Statist., Volume 19, Number 2 (1991), 741-759.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Mammen, Enno. Nonparametric Regression Under Qualitative Smoothness Assumptions. Ann. Statist. 19 (1991), no. 2, 741--759. doi:10.1214/aos/1176348118. https://projecteuclid.org/euclid.aos/1176348118