In small area estimation, it is sometimes necessary to use model-based methods to produce estimates in areas with little or no data. In official statistics, we often require that some aggregate of small area estimates agree with a national estimate for internal consistency purposes. Enforcing this agreement is referred to as benchmarking, and while methods currently exist to perform benchmarking, few are ideal for applications with non-normal outcomes and benchmarks with uncertainty. Fully Bayesian benchmarking is a theoretically appealing approach insofar as we can obtain posterior distributions conditional on a benchmarking constraint. However, existing implementations may be computationally prohibitive. In this paper, we critically review benchmarking methods in the context of small area estimation in low- and middle-income countries with binary outcomes and uncertain benchmarks, and propose a novel approach in which an unbenchmarked method that produces area-level samples can be combined with a rejection sampler or Metropolis-Hastings algorithm to produce benchmarked posterior distributions in a computationally efficient way. To illustrate the flexibility and efficiency of our approach, we provide comparisons to an existing benchmarking approach in a simulation, and applications to HIV prevalence and under-5 mortality estimation. Code implementing our methodology is available in the R package stbench.
翻译:在小面积估算方面,有时有必要使用基于模型的方法来对数据少或没有数据的地区进行估算。在官方统计中,我们常常要求小面积估算的某些总量与国内一致性目的的国家估算一致。执行这一协议被称为基准,尽管目前存在基准制定方法,但对于非正常结果和不确定的基准应用来说,没有什么理想。完全的巴伊西亚基准是一种理论上有吸引力的方法,只要我们能够以基准限制为条件获得后继分配;然而,现有的实施可能在计算上令人望而却步。在本文件中,我们严格审查中低收入国家小面积估算中具有二元结果和不确定基准的小面积估算基准方法,并提出一种新的方法,即制作地区级样本的无标志方法可以与拒绝采样者或Metopolis-Hastings算法相结合,以便以高效的计算方式制作基准后继分配。为了说明我们的方法的灵活性和效率,我们在模拟中对现有基准制定方法进行了比较,并应用了艾滋病毒流行率和5岁以下死亡率估算方法。在R标准中可以采用的方法。