Robust Bayesian small area estimation based on quantile regression

Quantile and M-quantile regression have been applied successfully to small area estimation within the frequentist approach. Quantile regression is applied in the same context but from a Bayesian perspective. Joint modelling of the quantile function is considered, adopting a non parametric assumption on the data generating process that nonetheless explicitly includes the normal distribution as a special case. A specification of the random part of the model that is simple and consistent with the predictive aim of small area estimation is proposed. Although the main output of the method is the estimation of the whole quantile function, estimators of the small area means based on the integration of the quantile function are proposed and discussed. A simulation exercise is used to assess the frequentist properties of these proposed predictors, that result at least as efficient as frequentist small area estimators based on quantile regression in scenarios characterized by the presence of outliers. The proposed method is illustrated using data from the European survey on Income and Living Conditions (EU-SILC).