Abstract

Area-level approaches play a central role in small area estimation, but their use typically depends on strong distributional assumptions and on the availability of accurate design-based variance estimates. In practice, these requirements are often unrealistic: small area sample sizes make the direct variance estimates unstable, and the assumption of normal random effects can be too restrictive. Building on recent work extending the M-quantile methods to area-level data, we identify important limitations due to untrustworthy variance estimates in small areas. To overcome these issues, we propose a new class of M-quantile area-level models that relaxes both the normality assumption and the need for reliable design-based variances. The approach is illustrated with Spanish data, showing clear practical advantages confirmed by simulation studies. Acknowledgements: This research is part of the Juan de la Cierva fellowship (ref. JDC2024-053513-I) funded by the Ministerio de Ciencia, Innovación y Universidades (MICIU/AEI/10.13039/501100011033) and co-funded by the European Social Fund Plus (FSE+). It has also been supported by the Xunta de Galicia (Competitive Reference Groups ED431C-2024/14) and by MODES and CITIC, as a center accredited for excellence within the Galician University System and a member of the CIGUS Network, receives subsidies from the Department of Education, Science, Universities, and Vocational Training of the Xunta de Galicia. Additionally, it is co-financed by the EU through the FEDER Galicia 2021-27 operational program (Ref. ED431G 2023/01).