Nonparametric regression under qualitative smoothness assumptions
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_\infty or L2L2L_2 norm, we consider the class of functions whose (m−1)(m−1)(m - 1)st derivative consists of at most kkk m...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
1991
|
| In: |
The annals of statistics
Year: 1991, Volume: 19, Issue: 2, Pages: 741-759 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176348118 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1176348118 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1176348118 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1176348118 
|
| Author Notes: | Enno Mammen |
| Summary: | 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_\infty 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. |
|---|---|
| Item Description: | First available in Project Euclid: 12 April 2007 Gesehen am 27.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176348118 |