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The use of a three‐level M ‐quantile model to map poverty at local administrative unit 1 in Poland
Author(s) -
Marchetti Stefano,
Beręsewicz Maciej,
Salvati Nicola,
Szymkowiak Marcin,
Wawrowski Łukasz
Publication year - 2018
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12349
Subject(s) - small area estimation , quantile , quantile regression , outlier , econometrics , estimation , estimator , statistics , poverty , unit (ring theory) , european union , mathematics , economics , economic growth , mathematics education , management , economic policy
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.