Small area estimation of poverty proportions under heteroscedastic Fay-Herriot models

Abstract

This paper presents a modification of the Fay-Herriot model that does not assume the homoscedasticity hypothesis of the random effects. To do this, it linearly explains a transformation of its variance from auxiliary variables. The new heteroscedastic model is more flexible and generally allows a better fit to the data. The mathematical foundations of the model are introduced, including fitting algorithms, small area linear indicator predictors, and mean square error estimators. Through simulation experiments, the behavior of the introduced algorithms, predictors and estimators is empirically studied. An application to real data from the Spanish Living Conditions Survey of 2022 is given. The target is the estimation of domain proportions of people under the poverty threshold by province and sex.