Small area estimation based on a multivariate Normal mixture model

I. Molina Peralta, A. Bikauskaite, D. Morales

Direct estimation methods may not be appropriate for small areas due to insufficient sample sizes. Efficiency can be improved by "borrowing strength" from other areas through models that employ auxiliary information at the area and/or unit level. We propose to estimate general small area parameters, including poverty indicators, using an empirical best (EB) estimator based on a multivariate normal mixture model that generalizes the usual nested error linear regression model. An expectation-maximization (EM) method is designed for maximum-likelihood fitting of the proposed mixture model. Small sample properties of the proposed EB estimator are analyzed by simulation studies and results are applied to estimate poverty indicators. A parametric bootstrap method is used for mean squared error estimation.

Keywords: EM method; Empirical best; Mixture model; Parametric Bootstrap

M. J. Lombardía Cortiña, M. D. Esteban Lefler, E. López Vizcaíno, D. Morales González, A. Pérez Martín

D. Morales González, J. P. Burgard, M. D. Esteban Lefler, A. Pérez Martín