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A Simple Variance Estimator for Unequal Probability Sampling without Replacement

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  • Yves Berger

Abstract

Survey sampling textbooks often refer to the Sen-Yates-Grundy variance estimator for use with without-replacement unequal probability designs. This estimator is rarely implemented because of the complexity of determining joint inclusion probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen-Hurwitz with replacement variance estimator; which often leads to overestimation of the variance for large sampling fractions that are common in business surveys. We will consider an alternative estimator: the Hajek (1964) variance estimator that depends on the first-order inclusion probabilities only and is usually more accurate than the Hansen-Hurwitz estimator. We review this estimator and show its practical value. We propose a simple alternative expression; which is as simple as the Hansen- Hurwitz estimator. We also show how the Hajek estimator can be easily implemented with standard statistical packages.

Suggested Citation

  • Yves Berger, 2004. "A Simple Variance Estimator for Unequal Probability Sampling without Replacement," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 305-315.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:3:p:305-315
    DOI: 10.1080/0266476042000184046
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    Cited by:

    1. Xavier D'haultfoeuille & Fabien Dell, 2008. "Measuring the Evolution of Complex Indicators: Theory and Application to the Poverty Rate in France," Annals of Economics and Statistics, GENES, issue 90, pages 259-290.
    2. A. Sikov & J. M. Stern, 2019. "Application of the full Bayesian significance test to model selection under informative sampling," Statistical Papers, Springer, vol. 60(1), pages 89-104, February.
    3. Xin Zhao & Anton Grafström, 2024. "Estimation of change with partially overlapping and spatially balanced samples," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.

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