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 purpose of improving its small sample efficiency while preserving good robustness level. It has been published for linear model and is now extended to GLM. Monte Carlo experiments are used explore performance this extension in Poisson regression case. Several candidates DCML compared; modified conditional starting very minimum density power divergence selected as best candidate. shown empirically that remarkably improves without loss robustness. An example using real hospital length stay data fitted by negative binomial discussed.