Model-based Properties of Replication Variance Estimators for Sample Surveys

有限总体调查中的重复方差估计是调查统计学家和研究人员的标准工具。 最常用的两种方法是折刀法和平衡重复复制法（BRR）。 当复制方法以教科书和期刊文章中描述的标准方式实现时，有大量的理论可用于复制方法。 然而，在实践中，这些方法的操作方式往往不符合标准的理论要求。 例如，在折刀法中，基本方法是删除一个第一阶段样本单元，基于剩余样本单元计算估计值，循环所有第一阶段样本单元，并计算所得估计值集合之间的方差。 在实践中，通过在层内或跨层组合单元来形成单元组。 然后，整个组被丢弃，以计算一个刀切方差估计。 本项目将评估实际使用的方法，并调查使用基于模型的有限总体抽样方法对现有方法的潜在改进。 特别是，这项工作将研究权重调整分组刀切，并在较小程度上，部分平衡BRR和基于模型的属性，这两种方法的方差估计。 总体总数的一般回归估计和其他非线性估计将被强调。这些分组方法的理论是有限的，并且不清楚实际使用的方法总是具有良好的理论性质。 由于数据库的构建方式，重复方差估计的不良实施的后果可能是重要的。 完整样本和子样本（或重复样本）的权重由数据库构造函数创建，该构造函数将权重附加到数据库中的每条记录。 然后，用户被指示使用这些权重来计算所有统计数据的方差，无论多么复杂。 如果创建的重复权重集不佳，则会影响所有分析师。 这项研究旨在指导如何在调查中实施这些分组方法，特别是关于经济、人口健康状况和社会科学中其他应用的调查。 这项研究得到了方法、测量和统计方案、统计和概率方案以及联邦统计机构联盟的支持，作为支持调查和统计方法研究的联合活动的一部分。

Replication variance estimation in surveys of finite populations is a standard tool of survey statisticians and researchers. Two of the most common methods used are the jackknife and balanced repeated replication (BRR). There is a substantial amount of theory available for the replication methods when they are implemented in standard ways described in textbooks and journal articles. In practice, however, these methods are operationalized in ways that often do not fit the standard theoretical requirements. In the jackknife, for example, the basic approach is to delete one first-stage sample unit, compute an estimate based on the remaining sample units, cycle through all first-stage sample units, and compute a variance among the resulting set of estimates. In practice, groups of units are formed by combining units within or across strata. Entire groups are then dropped-out in order to compute a jackknife variance estimate. This project will evaluate methods used in practice and investigate potential improvements to current methods using the model-based approach to finite population sampling. In particular, this work will study weight adjustments in the grouped jackknife and, to a lesser extent, partially balanced BRR and model-based properties of these two methods of variance estimation. The general regression estimator of population totals and other nonlinear estimators will be emphasized.Theory for these grouped methods is limited, and it is unclear that the methods used in practice always have good theoretical properties. The ramifications of poor implementation of replicate variance estimation can be important because of the way that data bases are constructed. Weights for the full sample and for subsamples (or replicates) are created by the database constructor who appends the weights to each record in the database. Users are then instructed to use those weights to compute variances for all statistics, regardless of how complex. If a poor set of replicate weights is created, this affects all analysts. The research is intended to provide guidance on how to implement these grouped methods in surveys, particularly ones concerning the economy, health status of the population, and other applications in the social sciences. This 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.