Improving the Efficiency of Robust Estimators for the Generalized Linear Model
The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/4/1/8 |
| _version_ | 1827603739982168064 |
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| author | Alfio Marazzi |
| author_facet | Alfio Marazzi |
| author_sort | Alfio Marazzi |
| collection | DOAJ |
| description | The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared; the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed. |
| first_indexed | 2024-03-09T05:45:46Z |
| format | Article |
| id | doaj.art-13a49c69d57e405cbc4f267f62bee09b |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-09T05:45:46Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-13a49c69d57e405cbc4f267f62bee09b2023-12-03T12:20:55ZengMDPI AGStats2571-905X2021-02-01418810710.3390/stats4010008Improving the Efficiency of Robust Estimators for the Generalized Linear ModelAlfio Marazzi0Nice Computing SA, 1052 Le Mont-sur-Lausanne, SwitzerlandThe distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared; the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed.https://www.mdpi.com/2571-905X/4/1/8robust GLM estimatorsrobust Poisson regressionconditional maximum likelihood estimatorminimum density power divergence estimatordistance constrained maximum likelihood |
| spellingShingle | Alfio Marazzi Improving the Efficiency of Robust Estimators for the Generalized Linear Model Stats robust GLM estimators robust Poisson regression conditional maximum likelihood estimator minimum density power divergence estimator distance constrained maximum likelihood |
| title | Improving the Efficiency of Robust Estimators for the Generalized Linear Model |
| title_full | Improving the Efficiency of Robust Estimators for the Generalized Linear Model |
| title_fullStr | Improving the Efficiency of Robust Estimators for the Generalized Linear Model |
| title_full_unstemmed | Improving the Efficiency of Robust Estimators for the Generalized Linear Model |
| title_short | Improving the Efficiency of Robust Estimators for the Generalized Linear Model |
| title_sort | improving the efficiency of robust estimators for the generalized linear model |
| topic | robust GLM estimators robust Poisson regression conditional maximum likelihood estimator minimum density power divergence estimator distance constrained maximum likelihood |
| url | https://www.mdpi.com/2571-905X/4/1/8 |
| work_keys_str_mv | AT alfiomarazzi improvingtheefficiencyofrobustestimatorsforthegeneralizedlinearmodel |