Local Linear Smoothing in Additive Models as Data Projection
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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. red. / Denis Belomestny; Cristina Butucea; Enno Mammen; Eric Moulines; Markus Reiß; Vladimir V. Ulyanov. Springer, 2023. s. 197-223 (Springer Proceedings in Mathematics and Statistics, Bind 425).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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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