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.
Highlights
For a long time, early robust parametric procedures were unable to combine a high level of outlier-resistance and a high level of efficiency under the model
We introduced a simple modification of the original distance constrained maximum likelihood procedure (DCML) that can be used for the generalized linear model (GLM)
The new DCML is defined as the convex combination of the robust and the maximum likelihood (ML) estimator that minimizes a quadratic distance from the ML estimator under the constraint that the distance from the robust estimator is smaller than a given bound δ
Summary
Early robust parametric procedures were unable to combine a high level of outlier-resistance and a high level of efficiency under the model. Several robust methods for the generalized linear model (GLM) have been proposed. [17] proposed a regression estimator with the maximum breakdown point and high finite sample efficiency. [18] introduced a general method to improve the finite sample efficiency of a robust estimator. It turns out that the final estimator is a convex combination of the robust and the maximum likelihood estimator. The modification exploits only the most crucial elements of the original proposal: it directly defines the DCML as a convex combination of the robust and the ML estimator and uses a quadratic distance between the coefficients. We explore the performance of the DCML method by means of Monte Carlo experiments considering some well-known robust estimators, for which the public domain R software is available, as initial estimators. We describe a bootstrap experiment with real hospital length of stays fitted by a negative binomial regression model
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