In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.

中文翻译：

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单一嵌套回归模型下小面积均值的基准估计量

在本文中，我们基于单位级别的模型修改了小面积估计量，以便将它们加在一起，得出可靠的更高级别的总体人口估计值。这些修改导致基准化的小面积估算器。我们考虑两种基准程序。一种基于用适当的变量扩充单元级模型的方法。另一种方法是使用直接估算器的校准权重，这些标定权重在较高级别上是可靠的。这些权重用于估计器中，这些估计器基于每个小区域的单位级别模型的汇总。通过适当地修改与相应的非基准估计量相关联的均方误差估计量，可以得出建议的基准估计量的均方误差估计量。估计器的属性通过仿真进行评估。