Local Linear Smoothing in Additive Models as Data Projection
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
We discuss local linear smooth backfitting for additive nonparametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each component of an additive model with the same asymptotic accuracy as if the other components were known. The asymptotic discussion of local linear smooth backfitting is rather complex because typically an overwhelming notation is required for a detailed discussion. In this paper we interpret the local linear smooth backfitting estimator as a projection of the data onto a linear space with a suitably chosen semi-norm. This approach simplifies both the mathematical discussion as well as the intuitive understanding of properties of this version of smooth backfitting.
Original language | English |
---|---|
Title of host publication | Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny |
Editors | Denis Belomestny, Cristina Butucea, Enno Mammen, Eric Moulines, Markus Reiß, Vladimir V. Ulyanov |
Number of pages | 27 |
Publisher | Springer |
Publication date | 2023 |
Pages | 197-223 |
ISBN (Print) | 9783031301131 |
DOIs | |
Publication status | Published - 2023 |
Event | International conference on Foundations of Modern Statistics, FMS 2019 - Berlin, Germany Duration: 6 Nov 2019 → 8 Nov 2019 |
Conference
Conference | International conference on Foundations of Modern Statistics, FMS 2019 |
---|---|
Land | Germany |
By | Berlin |
Periode | 06/11/2019 → 08/11/2019 |
Series | Springer Proceedings in Mathematics and Statistics |
---|---|
Volume | 425 |
ISSN | 2194-1009 |
Bibliographical note
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
- Additive models, Backfitting, Data projection, Kernel smoothing, Local linear estimation
Research areas
Links
- https://arxiv.org/pdf/2201.10930.pdf
Submitted manuscript
ID: 369291853