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Title: Controlling the bias for M-quantile estimators for small area Authors:  Gaia Bertarelli - University of Pisa (Italy)
Raymond Chambers - University of Wollongong (Australia)
David Haziza - Université de Montréal (Canada)
Nicola Salvati - University of Pisa (Italy)
Francesco Schirripa Spagnolo - Università di Pisa - Dipartimento di Economia e Management (Italy) [presenting]
Abstract: When representative outlier units are a concern for estimation of population quantities, it is essential to pay attention to them in a small area estimation (SAE) context, where sample sizes are very small and the estimation in often model-based. Standard approaches use plug-in robust prediction replacing parameter estimates in optimal but outlier-sensitive predictors by outlier robust versions (robust-projective approach). These predictors are efficient under the correct model. Still, they may be sensitive to the presence of outliers because they use plug-in robust prediction, which usually leads to a low prediction variance and a considerable prediction bias. DA bias correction method for models with continuous response variables has been proposed. We apply two general methods to reduce the prediction bias of the robust M-quantile predictors in SAE. The first estimator is based on the concept of conditional bias and extends previous results. The second one is a unified approach to M-quantile predictors based on a full bias correction. A Monte-Carlo simulation study is conducted. Results confirm that our approaches improve the efficiency and reduce the prediction bias of M-quantile predictors when the population contains units that may be influential if selected in the sample. Data from the EU-SILC 2017 survey in Italy are analysed.