Design Consistent Small Area Estimators Based on M-quantile Regression
Enrico Fabrizi1, Monica Pratesi2, Nicola Salvati2, Nikos Tzavidis3
1DISES, Catholic University, Piacenza, Italy; 2DSMAE, University of Pisa, Italy; 3School of Social Sciences, University of Southampton, United Kingdom

Small area estimators based on M-quantile regression have been recently introduced by Chambers and Tzavidis (2006) and Tzavidis et al. (2010). The aim of those papers is to obtain reliable small area estimates robust with respect to the presence of outliers and without the use of demanding distributional assumptions typical of the predictors based on random effects models. These M-quantile predictors, however, do not make use of the unit level survey weights and, as a result, they are not design consistent as the area sample sizes become large, unless the sampling design is self-weighting within areas. In this paper we adopt a model assisted approarch and we develop design consistent small area estimators based on the M-quantile small area model. Analytic and bootstrap estimator of the design-based MSE are discussed. The proposed estimators are empirically evaluated in the presence of complex sampling designs.

Keywords: Finite populations descriptive quantities; Sampling weights; Robust estimation; Design-based inference

Biography: Enrico Fabrizi is a researcher in Business and Economics Statistics (Statistica Economica). He holds a PhD in Statistics from the Department of Statistics, University of Bologna. He has research interests in survey sampling methodology, Bayesian inference applied to the analysis of complex survey data, small area estimation, with special focus on estimation of poverty related parameters. Before his current position at the UCSC, he has worked at the University of Bologna, Dept. of Statistics, and at the University of Bergamo (Dept. of Mathematics and Statistics).