Prediction of Poverty Proportions Under Random Regression Coefficients Two-Fold Fay-Herriot Models

Abstract

[Abstract] Using a two-fold Fay-Herriot model with random intercepts and random regression coefficients, we develop area-level predictors for poverty proportions and propose both analytic and bootstrap-based estimators for the mean squared error. Model parameters are estimated via residual maximum likelihood, and empirical best linear unbiased predictors are used for random effects. To assess the performance of the estimation algorithm, predictors, and mean squared error estimators, we conduct simulation studies. The proposed methodology is applied to data from the 2022 Spanish Living Conditions Survey to estimate poverty proportions at the provincial level, disaggregated by gender and age group. This study offers a robust and innovative framework for small-area estimation, enabling detailed poverty mapping with accurate estimates and reliable uncertainty measures.