Robust Small Area Prediction for Counts

A new semiparametric approach to model-based small area prediction for counts is proposed and used for estimating the average number of visits to physicians for Health Districts in Central Italy. The proposed small area predictor is based on defining an M-quantile model for count data by extending the ideas in Cantoni and Ronchetti (2001) and Chambers & Tzavidis (2006). This predictor can be viewed as an outlier robust alternative to the more commonly used Empirical Plug-in Predictor that is based on a Poisson generalised linear mixed model with Gaussian random effects. Results from the real data application and from a simulation experiment confirm that the proposed small area predictor has good robustness properties and in some cases can be more efficient than alternative small area approaches.