The use of a three level M-quantile model to map poverty at LAU 1 in Poland

A three-level M-quantile model for small area estimation is proposed. The methodology represents an efficient alternative to prediction by using a three-level linear mixed model in the presence of outliers and it is based on an extension of M-quantile regression. A modified method of the traditionalM-quantile (two-level) approach for poverty estimation is also proposed. In addition, an estimator of the mean-squared prediction error is described, which is based on a bootstrap procedure. The methodology proposed, as well as the three-level empirical best predictor, are applied to Polish European Union Survey on Income and Living Conditions and census data to estimate poverty at local administrative unit 1 level in Poland, i.e. the level for which the Central Statistical Office of Poland has not published any official estimates to date.