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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01621459_v106_n494_p661_Bergesio |
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todo:paper_01621459_v106_n494_p661_Bergesio2023-10-03T15:01:31Z Projection estimators for generalized linear models Bergesio, A. Yohai, V.J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, A. Yohai, V.J. 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. |
| format |
JOUR |
| author |
Bergesio, A. Yohai, V.J. |
| author_facet |
Bergesio, A. Yohai, V.J. |
| author_sort |
Bergesio, A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_01621459_v106_n494_p661_Bergesio |
| work_keys_str_mv |
AT bergesioa projectionestimatorsforgeneralizedlinearmodels AT yohaivj projectionestimatorsforgeneralizedlinearmodels |
| _version_ |
1807320783112896512 |