Methodological Advances in Robust Small Area Estimation

Abstract

[Abstract]: Small Area Estimation techniques address the growing demand for reliable disaggregated statistics by fitting models to unit-level or area-level data. While recent advances in unit-level mixed models are significant, the presence of outliers has driven the development of robust methods. M-quantile regression offers a promising alternative to mixed models for Small Area Estimation, though some theoretical aspects remain underexplored. We cover the optimal selection of the robustness parameters for bias correction, improving outlier detection. In addition, we propose bootstrap methods to approximate the distribution of area-specific M-quantile coefficients and optimal robustness parameters, enhancing inference and diagnostics.