Local Linear Smoothing in Additive Models as Data Projection

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Standard

Local Linear Smoothing in Additive Models as Data Projection. / Hiabu, Munir; Mammen, Enno; Meyer, Joseph T.

Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny. ed. / Denis Belomestny; Cristina Butucea; Enno Mammen; Eric Moulines; Markus Reiß; Vladimir V. Ulyanov. Springer, 2023. p. 197-223 (Springer Proceedings in Mathematics and Statistics, Vol. 425).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Harvard

Hiabu, M, Mammen, E & Meyer, JT 2023, Local Linear Smoothing in Additive Models as Data Projection. in D Belomestny, C Butucea, E Mammen, E Moulines, M Reiß & VV Ulyanov (eds), Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny. Springer, Springer Proceedings in Mathematics and Statistics, vol. 425, pp. 197-223, International conference on Foundations of Modern Statistics, FMS 2019, Berlin, Germany, 06/11/2019. https://doi.org/10.1007/978-3-031-30114-8_5

APA

Hiabu, M., Mammen, E., & Meyer, J. T. (2023). Local Linear Smoothing in Additive Models as Data Projection. In D. Belomestny, C. Butucea, E. Mammen, E. Moulines, M. Reiß, & V. V. Ulyanov (Eds.), Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny (pp. 197-223). Springer. Springer Proceedings in Mathematics and Statistics Vol. 425 https://doi.org/10.1007/978-3-031-30114-8_5

Vancouver

Hiabu M, Mammen E, Meyer JT. Local Linear Smoothing in Additive Models as Data Projection. In Belomestny D, Butucea C, Mammen E, Moulines E, Reiß M, Ulyanov VV, editors, Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny. Springer. 2023. p. 197-223. (Springer Proceedings in Mathematics and Statistics, Vol. 425). https://doi.org/10.1007/978-3-031-30114-8_5

Author

Hiabu, Munir ; Mammen, Enno ; Meyer, Joseph T. / Local Linear Smoothing in Additive Models as Data Projection. Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny. editor / Denis Belomestny ; Cristina Butucea ; Enno Mammen ; Eric Moulines ; Markus Reiß ; Vladimir V. Ulyanov. Springer, 2023. pp. 197-223 (Springer Proceedings in Mathematics and Statistics, Vol. 425).

Bibtex

@inproceedings{f8892b762a8d4ba581ab519fa89d16f0,
title = "Local Linear Smoothing in Additive Models as Data Projection",
abstract = "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.",
keywords = "Additive models, Backfitting, Data projection, Kernel smoothing, Local linear estimation",
author = "Munir Hiabu and Enno Mammen and Meyer, {Joseph T.}",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; International conference on Foundations of Modern Statistics, FMS 2019 ; Conference date: 06-11-2019 Through 08-11-2019",
year = "2023",
doi = "10.1007/978-3-031-30114-8_5",
language = "English",
isbn = "9783031301131",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "197--223",
editor = "Denis Belomestny and Cristina Butucea and Enno Mammen and Eric Moulines and Markus Rei{\ss} and Ulyanov, {Vladimir V.}",
booktitle = "Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny",
address = "Germany",

}

RIS

TY - GEN

T1 - Local Linear Smoothing in Additive Models as Data Projection

AU - Hiabu, Munir

AU - Mammen, Enno

AU - Meyer, Joseph T.

N1 - Publisher Copyright: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Additive models

KW - Backfitting

KW - Data projection

KW - Kernel smoothing

KW - Local linear estimation

UR - http://www.scopus.com/inward/record.url?scp=85169032204&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-30114-8_5

DO - 10.1007/978-3-031-30114-8_5

M3 - Article in proceedings

AN - SCOPUS:85169032204

SN - 9783031301131

T3 - Springer Proceedings in Mathematics and Statistics

SP - 197

EP - 223

BT - Foundations of Modern Statistics - Festschrift in Honor of Vladimir Spokoiny

A2 - Belomestny, Denis

A2 - Butucea, Cristina

A2 - Mammen, Enno

A2 - Moulines, Eric

A2 - Reiß, Markus

A2 - Ulyanov, Vladimir V.

PB - Springer

T2 - International conference on Foundations of Modern Statistics, FMS 2019

Y2 - 6 November 2019 through 8 November 2019

ER -

ID: 369291853