The Use of a Three-LevelM-Quantile Model to Map Poverty at Local Administrative Unit 1 in Poland
提出一种三水平M分位数模型用于小区域估计，能有效处理异常值，并应用于波兰收入与生活条件调查和普查数据，估计地方行政单元1的贫困水平。
Summary 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 traditional M-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.