Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects

This paper introduces a temporal bivariate area-level linear mixed model with independent time effects for estimating small area socioeconomic indicators. The model is fitted by using the residual maximum likelihood method. Empirical best linear unbiased predictors of these indicators are derived. An approximation to the matrix of mean squared errors (MSE) is given and four MSE estimators are proposed. The first MSE estimator is a plug-in version of the MSE approximation. The remaining MSE estimators rely on parametric bootstrap procedures. Three simulation experiments designed to analyze the behavior of the fitting algorithm, the predictors and the MSE estimators are carried out. An application to real data from the 2005 and 2006 Spanish living conditions survey illustrate the introduced statistical methodology. The target is the estimation of 2006 poverty proportions and gaps by provinces and sex.