Empirical best predictors under multivariate Fay-Herriot models and their numerical approximation

Abstract

Small area estimation of multivariable non-linear domain indicators using aggregated data is addressed. By assuming that the target vector follows a multivariate Fay-Herriot model, empirical best predictors of domain parameters that are arbitrary Lebesgue-measurable functions of multiple target variables are derived. In this context, Monte Carlo and Gauss-Hermite quadrature methods for integral approximation are discussed. A parametric bootstrap algorithm for mean squared error estimation is presented. Simulation experiments are conducted to study the behaviour of the introduced methodology. Moreover, an illustrative application to real data from the Spanish labour force survey is provided. In this example, province-level unemployment rates, crossed by age classes and sex, are estimated.