Outlier robust model-assisted small area estimation

Small area estimation with M-quantile models was proposed by Chambers and Tzavidis (2006). The key target of this approach to small area estimation is to obtain reliable and outlier robust estimates avoiding at the same time the need for strong parametric assumptions. This approach, however, does not allow for the use of unit level survey weights, making questionable the design consistency of the estimators unless the sampling design is self-weighting within small areas. In this paper, we adopt a model-assisted approach and construct design consistent small area estimators that are based on the M-quantile small area model. Analytic and bootstrap estimators of the design-based variance are discussed. The proposed estimators are empirically evaluated in the presence of complex sampling designs.