A range of data is of geographic interest but is not available at a small area level from existing data sources. Small area estimation (SAE) offers techniques to estimate population parameters of target variables to detailed scales based on relationships between those target variables and relevant auxiliary variables. The resulting indirect small area estimate can deliver a lower mean squared error compared to its direct survey estimate, given that variance can be reduced markedly even if bias increases. Spatial microsimulation SAE approaches are widely utilized but only beginning to engage with the potential of composite estimators that use a weighted combination of indirect and direct estimators to reduce further the mean squared error of the small area estimate compared to an indirect SAE estimator alone. This article advances these approaches by constructing for the first time in the microsimulation literature an optimal composite estimator for such SAE approaches in which the combining weight is calculated from the mean squared errors of the two estimators; thus, optimizing the reduction in MSE of the resulting small area estimates. This optimal composite estimator is demonstrated and evaluated in a model‐based simulation study and application based on the real data.

中文翻译：

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空间微观模拟小面积估计中最优组合估计器的开发与评估

一定范围的数据具有地理意义，但是在现有的数据源的小范围内无法使用。小面积估计（SAE）提供了根据目标变量和相关辅助变量之间的关系将目标变量的总体参数估计为详细比例的技术。考虑到即使偏差增加，方差也可以显着降低，因此得出的间接小区域估计值可以提供比其直接调查估计值更低的均方误差。空间微观模拟SAE方法得到了广泛的应用，但只是开始与使用间接和直接估计器的加权组合的复合估计器的潜力相提并论，与单独使用间接SAE估计器相比，该方法进一步减小了小面积估计的均方误差。本文通过在微观模拟文献中首次构建针对此类SAE方法的最佳复合估计器，从而从两个估计器的均方误差计算出合并权重，从而对这些方法进行了改进。因此，可以优化生成的小面积估算值的MSE降低。在基于模型的仿真研究和基于实际数据的应用中，论证并评估了这种最佳的综合估计量。