Spatial M-quantile Models for Small Area Estimation

In small area estimation direct survey estimates that rely only on area-specific data can exhibit large sampling variability due to small sample sizes at the small area level. Efficient small area estimates can be constructed using explicit linking models that borrow information from related areas. The most popular class of models for this purpose are models that include random area effects. Estimation for these models typically assumes that the random area effects are uncorrelated. In many situations, however, it is reasonable to assume that the effects of neighbouring areas are correlated. Models that extend conventional random effects models to account for spatial correlation between the small areas have been recently proposed in literature. A new semi-parametric approach to small area estimation is based on the use of M-quantile models. Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumptions and are robust to the presence of outliers. In its current form, however, the M-quantile approach to small area estimation does not allow for spatially correlated area effects. The aim of this paper is to extend the M-quantile approach to account for such spatial correlation between small areas.