Projection estimators for generalized linear models

We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We...

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Detalles Bibliográficos
Autor principal: Bergesio, Andrea Claudia
Publicado: 2011
Materias:
Logistic regression
Maximum bias
One-step estimators
Robust estimators
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v106_n494_p661_Bergesio
http://hdl.handle.net/20.500.12110/paper_01621459_v106_n494_p661_Bergesio
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01621459_v106_n494_p661_Bergesio
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spelling paper:paper_01621459_v106_n494_p661_Bergesio2023-06-08T15:13:37Z Projection estimators for generalized linear models Bergesio, Andrea Claudia Logistic regression Maximum bias One-step estimators Robust estimators We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε of outlier contamination. For small ε, this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors. Since these projection estimators are not asymptotically normal, we define one-step weighted M-estimators starting at the projection estimators. These estimators have the same asymptotic normal distribution as the M-estimator and a degree of robustness close to the one of the projection estimator. We perform a Monte Carlo simulation for the case of binomial and Poisson regression with canonical links. This study shows that the proposed estimators compare favorably with respect to other robust estimators. Supplemental Material containing the proofs and the numerical algorithm used to compute the P-estimator is available online. © 2011 American Statistical Association. Fil:Bergesio, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v106_n494_p661_Bergesio http://hdl.handle.net/20.500.12110/paper_01621459_v106_n494_p661_Bergesio
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Logistic regression
Maximum bias
One-step estimators
Robust estimators
spellingShingle Logistic regression
Maximum bias
One-step estimators
Robust estimators
Bergesio, Andrea Claudia
Projection estimators for generalized linear models
topic_facet Logistic regression
Maximum bias
One-step estimators
Robust estimators
description We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε of outlier contamination. For small ε, this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors. Since these projection estimators are not asymptotically normal, we define one-step weighted M-estimators starting at the projection estimators. These estimators have the same asymptotic normal distribution as the M-estimator and a degree of robustness close to the one of the projection estimator. We perform a Monte Carlo simulation for the case of binomial and Poisson regression with canonical links. This study shows that the proposed estimators compare favorably with respect to other robust estimators. Supplemental Material containing the proofs and the numerical algorithm used to compute the P-estimator is available online. © 2011 American Statistical Association.
author Bergesio, Andrea Claudia
author_facet Bergesio, Andrea Claudia
author_sort Bergesio, Andrea Claudia
title Projection estimators for generalized linear models
title_short Projection estimators for generalized linear models
title_full Projection estimators for generalized linear models
title_fullStr Projection estimators for generalized linear models
title_full_unstemmed Projection estimators for generalized linear models
title_sort projection estimators for generalized linear models
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v106_n494_p661_Bergesio
http://hdl.handle.net/20.500.12110/paper_01621459_v106_n494_p661_Bergesio
work_keys_str_mv AT bergesioandreaclaudia projectionestimatorsforgeneralizedlinearmodels
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