Small Area Income Estimation over Time via a Random Regression Coefficients Two-Fold Fay–Herriot Model

N. Diz Rosales, M. J. Lombardía Cortiña, D. Morales

Reliable small area income estimation remains difficult when survey data are sparse. We propose a hierarchical two-fold Fay-Herriot model with random regression coefficients that captures both temporal dependence (via AR(1) structure) and domain heterogeneity. The model borrows strength across areas and years, improving precision for domains with small sample sizes. Estimation uses residual maximum likelihood and empirical best linear unbiased predictors via Fisher scoring. Simulations show gains in robustness over standard two-fold Fay-Herriot models. Mean squared error is estimated analytically and via bootstrap; the analytic approach balances accuracy and efficiency. The method is applied to Spanish provincial income data (2013-2022), revealing persistent regional disparities and a widening post-pandemic gender gap.

Palabras clave: Fay-Herriot, public statistics, random slopes, temporary dependency

SI Estimación en áreas pequeñas
4 de septiembre de 2026  11:10
Aula 21

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