Small area estimation under a measurement error bivariate Fay-Herriot model

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

The bivariate Fay-Herriot model is an area-level linear mixed model for estimating domain means of two correlated target variables. In practice, the dependent variables are direct estimators calculated from survey data and the auxiliary variables are true domain means obtained from external data sources. Statistician may take auxiliary variables from alternative surveys and therefore they are measured with error. We introduce a bivariate Fay-Herriot model that takes into account the measurement error of the auxiliary variables, and give a fitting algorithm that calculate residual maximum likelihood estimates of the model parameters. Based on the new model, empirical best predictors of domain means are introduced and a parametric bootstrap procedure for estimating the mean squared error is proposed. We give an application to estimate poverty proportions and gaps in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.

Keywords: Multivariate models Fay-Herriot model small area estimation measurement error Monte Carlo simulation poverty proportion poverty gap.

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

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