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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10485252_v29_n4_p744_Boente |
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todo:paper_10485252_v29_n4_p744_Boente2023-10-03T15:58:36Z Robust estimators for additive models using backfitting Boente, G. Martínez, A. Salibián-Barrera, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Boente, G. Martínez, A. Salibián-Barrera, M. 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. |
| format |
JOUR |
| author |
Boente, G. Martínez, A. Salibián-Barrera, M. |
| author_facet |
Boente, G. Martínez, A. Salibián-Barrera, M. |
| author_sort |
Boente, G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10485252_v29_n4_p744_Boente |
| work_keys_str_mv |
AT boenteg robustestimatorsforadditivemodelsusingbackfitting AT martineza robustestimatorsforadditivemodelsusingbackfitting AT salibianbarreram robustestimatorsforadditivemodelsusingbackfitting |
| _version_ |
1807321300531675136 |