Model-based Properties of Replication Variance Estimators for Sample Surveys

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

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.