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Inference for two‐stage sampling designs

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  • Guillaume Chauvet
  • Audrey‐Anne Vallée

Abstract

Two‐stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with associated confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz–Thompson estimator are desirable, along with the consistency of associated variance estimators. These properties have been mainly studied for single‐stage sampling designs. In this work, we prove the consistency of the Horvitz–Thompson estimator and of associated variance estimators for a general class of two‐stage sampling designs, under mild assumptions. We also study two‐stage sampling with a large entropy sampling design at the first stage and prove that the Horvitz–Thompson estimator is asymptotically normally distributed through a coupling argument. When the first‐stage sampling fraction is negligible, simplified variance estimators which do not require estimating the variance within the primary sampling units are proposed and shown to be consistent. An application to a panel for urban policy, which is the initial motivation for this work, is also presented.

Suggested Citation

  • Guillaume Chauvet & Audrey‐Anne Vallée, 2020. "Inference for two‐stage sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 797-815, July.
  • Handle: RePEc:bla:jorssb:v:82:y:2020:i:3:p:797-815
    DOI: 10.1111/rssb.12368
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    References listed on IDEAS

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    1. Petter Brändén & Johan Jonasson, 2012. "Negative Dependence in Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 830-838, December.
    2. F. Jay Breidt & Jean D. Opsomer & Ismael Sanchez-Borrego, 2016. "Nonparametric Variance Estimation Under Fine Stratification: An Alternative to Collapsed Strata," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 822-833, April.
    3. Patrice Bertail & Emilie Chautru & Stephan Clémençon, 2017. "Empirical Processes in Survey Sampling with (Conditional) Poisson Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 97-111, March.
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