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Benchmarking techniques for reconciling Bayesian small area models at distinct geographic levels

机译：在不同地理级别调和贝叶斯小区域模型的基准化技术

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摘要

In sample surveys, there is often insufficient sample size to obtain reliable direct estimates for parameters of interest for certain domains. Precision can be increased by introducing small area models which 'borrow strength' by connecting different areas through use of explicit linking models, area-specific random effects, and auxiliary covariate information. One consequence of the use of small area models is that small area estimates at a lower (for example, county) geographic level typically will not aggregate to the estimate at the corresponding higher (for example, state) geographic level. Benchmarking is the statistical procedure for reconciling these differences. This paper provides new perspectives for the benchmarking problem, especially for complex Bayesian small area models which require Markov Chain Monte Carlo estimation. Two new approaches to Bayesian benchmarking are introduced: one procedure based on minimum discrimination information, and another procedure for fully Bayesian self-consistent conditional benchmarking. Notably the proposed procedures construct adjusted posterior distributions whose first and higher order moments are consistent with the benchmarking constraints. It is shown that certain existing benchmarked estimators are special cases of the proposed methodology under normality, giving a distributional justification for the use of benchmarked estimates. Additionally, a 'flexible' benchmarking constraint is introduced, where the higher geographic level estimate is not considered fixed, and is simultaneously adjusted, along with lower level estimates.
机译：在抽样调查中，通常没有足够的样本量来获得对某些领域感兴趣参数的可靠直接估计。通过引入小面积模型可以提高精度，这些小面积模型通过使用显式链接模型，特定于区域的随机效应和辅助协变量信息来连接不同区域，从而“借力”。使用小区域模型的一个结果是，较低（例如县）地理级别的小区域估计值通常不会汇总到相应较高（例如州）地理级别的估计值。标杆管理是调和这些差异的统计程序。本文为基准问题提供了新的视角，特别是对于需要马尔可夫链蒙特卡罗估计的复杂贝叶斯小面积模型。引入了两种新的贝叶斯基准测试方法：一种基于最小歧视信息的过程，另一种用于完全贝叶斯自洽条件条件基准测试的过程。值得注意的是，提出的程序构造了调整后验分布，其一阶和更高阶矩与基准约束一致。结果表明，某些现有的基准估计量是正常情况下拟议方法的特殊情况，从而为使用基准估计量提供了分配依据。另外，引入了“灵活的”基准约束，其中较高的地理级别估计不被认为是固定的，而是与较低的级别估计一起被同时调整。

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