Robust estimators for additive models using backfitting

Additive models provide an attractive setup to estimate regression functions in a nonparametric context. They provide a flexible and interpretable model, where each regression function depends only on a single explanatory variable and can be estimated at an optimal univariate rate. Most estimation p...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Fisher-consistency
kernel weights
robust estimation
smoothing
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v29_n4_p744_Boente
http://hdl.handle.net/20.500.12110/paper_10485252_v29_n4_p744_Boente
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10485252_v29_n4_p744_Boente
record_format dspace
spelling paper:paper_10485252_v29_n4_p744_Boente2023-06-08T16:01:20Z Robust estimators for additive models using backfitting Fisher-consistency kernel weights robust estimation smoothing Additive models provide an attractive setup to estimate regression functions in a nonparametric context. They provide a flexible and interpretable model, where each regression function depends only on a single explanatory variable and can be estimated at an optimal univariate rate. Most estimation procedures for these models are highly sensitive to the presence of even a small proportion of outliers in the data. In this paper, we show that a relatively simple robust version of the backfitting algorithm (consisting of using robust local polynomial smoothers) corresponds to the solution of a well-defined optimisation problem. This formulation allows us to find mild conditions to show Fisher consistency and to study the convergence of the algorithm. Our numerical experiments show that the resulting estimators have good robustness and efficiency properties. We illustrate the use of these estimators on a real data set where the robust fit reveals the presence of influential outliers. © 2017, © American Statistical Association and Taylor & Francis 2017. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v29_n4_p744_Boente http://hdl.handle.net/20.500.12110/paper_10485252_v29_n4_p744_Boente
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fisher-consistency
kernel weights
robust estimation
smoothing
spellingShingle Fisher-consistency
kernel weights
robust estimation
smoothing
Robust estimators for additive models using backfitting
topic_facet Fisher-consistency
kernel weights
robust estimation
smoothing
description Additive models provide an attractive setup to estimate regression functions in a nonparametric context. They provide a flexible and interpretable model, where each regression function depends only on a single explanatory variable and can be estimated at an optimal univariate rate. Most estimation procedures for these models are highly sensitive to the presence of even a small proportion of outliers in the data. In this paper, we show that a relatively simple robust version of the backfitting algorithm (consisting of using robust local polynomial smoothers) corresponds to the solution of a well-defined optimisation problem. This formulation allows us to find mild conditions to show Fisher consistency and to study the convergence of the algorithm. Our numerical experiments show that the resulting estimators have good robustness and efficiency properties. We illustrate the use of these estimators on a real data set where the robust fit reveals the presence of influential outliers. © 2017, © American Statistical Association and Taylor & Francis 2017.
title Robust estimators for additive models using backfitting
title_short Robust estimators for additive models using backfitting
title_full Robust estimators for additive models using backfitting
title_fullStr Robust estimators for additive models using backfitting
title_full_unstemmed Robust estimators for additive models using backfitting
title_sort robust estimators for additive models using backfitting
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v29_n4_p744_Boente
http://hdl.handle.net/20.500.12110/paper_10485252_v29_n4_p744_Boente
_version_ 1768543857166778368

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