Locally adaptive regression splines
Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to stud...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
1997
|
| In: |
The annals of statistics
Year: 1997, Volume: 25, Issue: 1, Pages: 387-413 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1034276635 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1034276635 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1034276635 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1034276635 
|
| Author Notes: | Enno Mammen, Sara van de Geer |
| Summary: | Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to study their asymptotic properties. In particular, these results imply that the estimates adapt well to spatially inhomogeneous smoothness. We show rates of convergence in bounded variation function classes and discuss pointwise limiting distributions. An iterative algorithm based on stepwise addition and deletion of knot points is proposed and its consistency proved. |
|---|---|
| Item Description: | First available in Project Euclid: 10 October 2002 Gesehen am 15.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1034276635 |