Poisson M-quantile regression for small area estimation

A new approach to model-based small area estimation for count outcomes 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 a Poisson M-quantile model by extending the ideas in Cantoni & Ronchetti (2001) and Chambers & Tzavidis (2006). This predictor can be viewed as a semi-parametric outlier robust alternative to the more commonly used plug-in Empirical Best 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 can be more efficient than alternative small area predictors.