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Estimation Under Cross-Classified Sampling With Application to a Childhood Survey

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  • Hélène Juillard
  • Guillaume Chauvet
  • Anne Ruiz-Gazen

Abstract

The cross-classified sampling design consists in drawing samples from a two-dimensional population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies in the French Longitudinal Survey on Childhood, by crossing a sample of maternity units and a sample of days. We propose to derive a general theory of estimation for this sampling design. We consider the Horvitz–Thompson estimator for a total, and show that the cross-classified design will usually result in a loss of efficiency as compared to the widespread two-stage design. We obtain the asymptotic distribution of the Horvitz–Thompson estimator and several unbiased variance estimators. Facing the problem of possibly negative values, we propose simplified nonnegative variance estimators and study their bias under a super-population model. The proposed estimators are compared for totals and ratios on simulated data. An application on real data from the French Longitudinal Survey on Childhood is also presented, and we make some recommendations. Supplementary materials for this article are available online.

Suggested Citation

  • Hélène Juillard & Guillaume Chauvet & Anne Ruiz-Gazen, 2017. "Estimation Under Cross-Classified Sampling With Application to a Childhood Survey," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 850-858, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:850-858
    DOI: 10.1080/01621459.2016.1186028
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    References listed on IDEAS

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    1. Skinner, C.J., 2015. "Cross-classified sampling: Some estimation theory," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 163-168.
    2. Skinner, C. J., 2015. "Cross-classified sampling: some estimation theory," LSE Research Online Documents on Economics 62261, London School of Economics and Political Science, LSE Library.
    3. Dalen, Jurgen & Ohlsson, Esbjorn, 1995. "Variance Estimation in the Swedish Consumer Price Index," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 347-356, July.
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    Cited by:

    1. Rivest, Louis-Paul & Ebouele, Sergio Ewane, 2020. "Sampling a two dimensional matrix," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).

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