Robust estimation in generalized linear models: the density power divergence approach

The generalized linear model is a very important tool for analyzing real data in several application domains where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. Quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases inference based on the maximum likelihood estimator could be unreliable. In this paper, we develop a robust estimation procedure for the generalized linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular special cases in detail-Poisson regression for count data and logistic regression for binary data. We will also illustrate the performance of the proposed estimators through some real-life examples.