Nonparametric regression under qualitative smoothness assumptions - Mammen, Enno (The annals of statistics, 1991)
We propose a new nonparametric regression estimate. In contrast to the traditional approach of considering regression functions whose mmmth derivatives lie in a ball in the L∞L∞L_∞ or L2L2L_2 norm, we consider the class of functions whose (m−1)(m−1)(m - 1)st derivative consists of at most kkk 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.
First available in Project Euclid: 12 April 2007
Gesehen am 27.02.2018