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Biometrika 2007 94(4):953-964; doi:10.1093/biomet/asm072
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© 2007 Biometrika Trust

Articles

A Jackknife Variance Estimator for Unistage Stratified Samples with Unequal Probabilities

Yves G. Berger

Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, SO17 1BJ, U.K. y.g.berger{at}soton.ac.uk

Received for publication 1 January 2005. Revision received 1 May 2007.
  Abstract

Existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities. A novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators. Under certain regularity conditions, the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities. The high entropy regularity condition necessary for consistency is shown to hold for the Rao–Sampford design. An empirical study of three unequal probability sampling designs supports our findings.

Key Words: Consistency • Design-based inference • Finite population correction • Sample survey • Smooth function of means • Stratification


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