Under a unit-level bivariate linear mixed model, this paper introduces small area predictors of expenditure means and ratios, and derives approximations and estimators of the corresponding mean squared errors. For the considered model, the REML estimation method is implemented. Several simulation experiments, designed to analyze the behavior of the introduced fitting algorithm, predictors and mean squared error estimators, are carried out. An application to real data from the Spanish household budget survey illustrates the behavior of the proposed statistical methodology. The target is the estimation of means of food and non-food household annual expenditures and of ratios of food household expenditures by Spanish provinces.

在单位水平的双变量线性混合模型下，本文引入了支出均值和比率的小面积预测因子，并推导了相应均方误差的近似值和估计量。对于所考虑的模型，实施了 REML 估计方法。进行了几个模拟实验，旨在分析引入的拟合算法、预测器和均方误差估计器的行为。对西班牙家庭预算调查的真实数据的应用说明了所提议的统计方法的行为。目标是估计西班牙各省的食品和非食品家庭年度支出以及食品家庭支出的比率。