The bivariate Fay–Herriot model is an area-level linear mixed model that can be used for estimating the domain means of two correlated target variables. Under this model, the dependent variables are direct estimators calculated from survey data and the auxiliary variables are true domain means obtained from external data sources. Administrative registers do not always give good auxiliary variables, so that statisticians sometimes take them from alternative surveys and therefore they are measured with error. We introduce a variant of the bivariate Fay–Herriot model that takes into account the measurement error of the auxiliary variables and we give fitting algorithms to estimate the model parameters. Based on the new model, we introduce empirical best predictors of domain means and we propose a parametric bootstrap procedure for estimating the mean squared error. We finally give an application to estimate poverty proportions and gaps in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.

双变量Fay-Herriot模型是区域级线性混合模型，可用于估计两个相关目标变量的域均值。在此模型下，因变量是根据调查数据计算出的直接估计量，辅助变量是从外部数据源获得的真实域均值。行政登记册并不总是能提供良好的辅助变量，因此统计人员有时会从其他调查中获取这些变量，因此对它们进行了错误的计量。我们引入了考虑到辅助变量的测量误差的双变量Fay-Herriot模型的变体，并给出了拟合算法来估计模型参数。基于新模型，我们介绍了域均值的经验最佳预测器，并提出了用于估计均方误差的参数自举程序。最后，我们将根据西班牙劳动力调查的辅助信息，在西班牙的生活条件调查中提供一个估算贫困率和差距的应用程序。