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Improving the Efficiency of Robust Estimators for the Generalized Linear Model

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  • Alfio Marazzi

    (Nice Computing SA, 1052 Le Mont-sur-Lausanne, Switzerland
    Faculty of Biology and Medicine, University of Lausanne, 1015 Lausanne, Switzerland)

Abstract

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.

Suggested Citation

  • Alfio Marazzi, 2021. "Improving the Efficiency of Robust Estimators for the Generalized Linear Model," Stats, MDPI, vol. 4(1), pages 1-20, February.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:1:p:8-107:d:492885
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    References listed on IDEAS

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    1. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.
    2. Alfio Marazzi & Marina Valdora & Victor Yohai & Michael Amiguet, 2019. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 223-241, March.
    3. Maronna, Ricardo A. & Yohai, Victor J., 2015. "High finite-sample efficiency and robustness based on distance-constrained maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 262-274.
    4. William H. Aeberhard & Eva Cantoni & Stephane Heritier, 2014. "Robust inference in the negative binomial regression model with an application to falls data," Biometrics, The International Biometric Society, vol. 70(4), pages 920-931, December.
    5. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    6. Howard D. Bondell & Leonard A. Stefanski, 2013. "Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 644-655, June.
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