This study examines issues of Small Area Estimation that are raised by reliance on the American Community Survey (ACS), which reports tract‐level data based on much smaller samples than the decennial census long‐form that it replaced. We demonstrate the problem using a 100% transcription of microdata from the 1940 census. By drawing many samples from two major cities, we confirm a known pattern: random samples yield unbiased point estimates of means or proportions, but estimates based on smaller samples have larger average errors in measurement and greater risk of large error. Sampling variability also inflates estimates of measures of variation across areas (reflecting segregation or spatial inequality). This variation is at the heart of much contemporary spatial analysis. We then evaluate possible solutions. For point estimates, we examine three Bayesian models, all of which reduce sampling variation, and we encourage use of such models to correct ACS small area estimates. However, the corrected estimates cannot be used to calculate estimates of variation, because smoothing toward local or grand means artificially reduces variation. We note that there are potential Bayesian approaches to this problem, and we demonstrate an efficacious alternative that uses the original sample data.

中文翻译：

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人口普查区小面积估计模型


本研究探讨了因依赖美国社区调查 (ACS) 而引发的小区域估计问题，该调查报告的区域级数据所基于的样本比它所取代的十年一次的人口普查长格式小得多。我们使用 1940 年人口普查的微观数据 100% 转录来演示该问题。通过从两个主要城市抽取许多样本，我们确认了一个已知的模式：随机样本产生均值或比例的无偏点估计，但基于较小样本的估计具有较大的平均测量误差和较大误差的风险。抽样变异性还会夸大对跨地区变异测量的估计（反映隔离或空间不平等）。这种变化是许多当代空间分析的核心。然后我们评估可能的解决方案。对于点估计，我们检查了三个贝叶斯模型，所有这些模型都减少了采样变异，并且我们鼓励使用此类模型来纠正 ACS 小区域估计。然而，校正后的估计不能用于计算变异估计，因为向局部或总体均值进行平滑会人为地减少变异。我们注意到这个问题有潜在的贝叶斯方法，并且我们展示了一种使用原始样本数据的有效替代方法。