Better Mean Estimation After Post-Stratification

• Activity Number: 445
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Jesse Frey* and Timothy Feeman
• Companies: Villanova University and Villanova University
• Keywords: Judgment post-stratification ; Lagrange multipliers ; Post-stratification ; Simple random sampling ; Stratified random sampling ; Taylor series approximation

Abstract

The standard population mean estimator for post-stratification is undefined when there are empty post-strata. In this paper, we develop a class of unbiased estimators that can be applied even with empty post-strata and that take into account the finite population correction factor. We first work under an assumption of equal post-stratum sizes, showing that which estimator is optimal in a given case depends only on the fraction of the total population variability that is in-stratum variability. We then extend the estimators to work in the more general case of unequal post-stratum sizes. In this more general case, we provide exact, simulation-based, and Taylor-series-based methods for determining how to appropriately weight each in-stratum mean. Our comparisons with existing estimators show that small but consistent efficiency gains are available from using the proposed estimators.