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Article

Improving the Efficiency of Robust Estimators for the Generalized Linear Model

by 1,2
1
Nice Computing SA, 1052 Le Mont-sur-Lausanne, Switzerland
2
Faculty of Biology and Medicine, University of Lausanne, 1015 Lausanne, Switzerland
Academic Editor: Marco Riani
Received: 2 December 2020 / Revised: 22 January 2021 / Accepted: 25 January 2021 / Published: 4 February 2021
(This article belongs to the Special Issue Robust Statistics in Action)
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. View Full-Text
Keywords: robust GLM estimators; robust Poisson regression; conditional maximum likelihood estimator; minimum density power divergence estimator; distance constrained maximum likelihood robust GLM estimators; robust Poisson regression; conditional maximum likelihood estimator; minimum density power divergence estimator; distance constrained maximum likelihood
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MDPI and ACS Style

Marazzi, A. Improving the Efficiency of Robust Estimators for the Generalized Linear Model. Stats 2021, 4, 88-107. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010008

AMA Style

Marazzi A. Improving the Efficiency of Robust Estimators for the Generalized Linear Model. Stats. 2021; 4(1):88-107. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010008

Chicago/Turabian Style

Marazzi, Alfio. 2021. "Improving the Efficiency of Robust Estimators for the Generalized Linear Model" Stats 4, no. 1: 88-107. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010008

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