Spatial and Small Area Estimation Problems with Application to Large-Scale Surveys

新的美国社区调查(ACS)每月接触全美约25万个家庭，收集了有关分布在美国各地的大量家庭的前所未有的大量信息。然而，即使有如此大的国家样本量，许多地理区域，如人口普查区域的样本量太小，估计值也不会有可接受的差异。该项目将产生新的小区域估计方法，这些方法利用ACS的空间结构和正在进行的数据收集，对ACS样本量不足的地理区域的贫困率等特征做出更准确的估计。一种新的具有连续变量和二元变量的多变量方法将结合来自不同地区、时间段和数据源的信息，在不增加数据收集成本的情况下产生更准确的小区域估计。新的多变量贝叶斯空间模型允许估计的非平稳性，将利用ACS中的空间信息来对数据中的空间和时间模式进行建模，改进小区域估计，并能够检测随着时间的变化。研究人员将研究计算机密集估计估计者均方误差的方法的特性，并开发数字稳定和计算高效的计算均方误差的方法。来自ACS的估计值用于收入和贫困评估、资金分配、交通规划、为残疾人分配资源、研究人口模式和迁移等许多目的。新的统计方法可望从区域协调委员会和其他具有空间信息的调查中提供更准确的小面积估计，从而提高可用于作出资源分配决定的信息的质量。这些方法还将使许多学科领域的研究人员能够利用调查数据的空间和时间方面来研究各种现象，如贫困的空间分布和局部不连续性、卡特里娜飓风等事件后的分布变化、其他数据集中测量的变量(例如环境污染物或犯罪受害者)与美国国家统计局数据之间的关系，以及交通模式的变化。统计方法可用于模拟污染物的空间分布，检测环境或引入的污染物，以及模拟教育干预的影响，以及许多其他应用。像ACS这样的大规模调查是昂贵的；在这个项目中开发的统计方法将帮助研究人员从他们那里提取更多的信息，而不需要额外的预算成本。作为支持调查和统计方法研究的联合活动的一部分，这项研究得到了方法学、测量和统计计划、统计和概率计划以及联邦统计机构联盟的支持。

The new American Community Survey (ACS), which contacts approximately 250,000 households across the United States each month, collects an unprecedented amount of information about a large number of households distributed spatially across the United States. Even with this large national sample size, however, the sample sizes in many geographic regions such as census tracts are too small for estimates to have acceptable variances. This project will result in new small area estimation methods that take advantage of the ACS's spatial structure and ongoing data collection to give more accurate estimates of characteristics such as poverty rate for geographic areas with insufficient ACS sample size. A new multivariate approach with continuous and binary variables will combine information from different regions, time periods, and data sources to yield more accurate small area estimates without additional data collection cost. New multivariate Bayesian spatial models, allowing nonstationarity in the estimation, will exploit the spatial information in the ACS to model spatial and temporal patterns in the data, improve small area estimates, and enable detection of changes over time. The investigators will study properties of computer-intensive methods for estimating mean squared errors of estimators, and develop numerically stable and computationally efficient methods for calculating mean squared errors.Estimates from the ACS are used for income and poverty assessments, funding allocation, transportation planning, allocation of resources for the disabled, studying population patterns and migration, and many other purposes. The new statistical methods are expected to give more precise small area estimates from the ACS and other surveys that have spatial information, thereby improving the quality of the information available for making resource allocation decisions. The methods also will allow researchers in many subject areas to take advantage of the spatial and temporal aspects of survey data to study phenomena such as spatial distribution and local discontinuities in poverty, distributional changes following events such as hurricane Katrina, relationships between variables measured in other data sets (for example, environmental contaminants or criminal victimization) and data from the ACS, and changes in transportation patterns. The statistical methods may be used to model the spatial distribution of pollutants, detect environmental or introduced contaminants, and model effects of interventions in education, among many other applications. Large-scale surveys such as the ACS are expensive; the statistical methods developed in this project will help researchers extract more information from them without additional budgetary costs. The research is supported by the Methodology, Measurement, and Statistics Program, the Statistics and Probability Program, and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.