Pseudo Empirical Multivariate Small Area Estimation of Domain Means

W. F. Acero Ruge, I. Molina Peralta, D. Morales

Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under unit-level models typically focus on a single response variable. This paper addresses the estimation of area means for several dependent target variables under a multivariate nested error regression (MNER) model. We propose a multivariate pseudo–empirical best linear unbiased predictor that accounts for the sampling mechanism. Moreover, by aggregating the MNER model, we derive a unified predictor that can be obtained from either unit-level or area-level data. Bootstrap procedures are proposed to estimate the mean squared errors (MSEs) of the proposed predictors. Simulation experiments are conducted to examine the properties of the proposed small area estimators and the MSE estimators.Finally, an application with housing data illustrates the proposed methods

Keywords: Design consistency, Empirical best linear unbiased predictor, Mean squared error, Parametric bootstrap

Mixed Models
September 2, 2026  11:20 AM
Aula 30

X. Espunya Soler, J. A. Sanchez Espigares, L. Acosta Argueta

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