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Sampling a two dimensional matrix

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  • Rivest, Louis-Paul
  • Ebouele, Sergio Ewane

Abstract

A new sampling design for populations whose units can be arranged as an N×M matrix is proposed. The sample must satisfy some constraints: row and column sample sizes are set in advance. The proposed sampling method gives the same selection probability to all the sample matrices that satisfy the constraints. Three algorithms to select a sample uniformly in the feasible set are presented: an exact algorithm based on the multivariate hypergeometric distribution, an MCMC algorithm, and the cube method. Their performances are evaluated using Monte Carlo simulations. The designs for sampling elements in a given row or a given column are investigated and the single inclusion and joint selection probabilities under the proposed design are evaluated. Several variance estimators are proposed for the Horvitz–Thompson estimator of the population mean of the survey variable y and their performances are compared in a Monte Carlo study. A numerical example dealing with a creel survey of fishermen found at 9 sites over 36 days is presented.

Suggested Citation

  • Rivest, Louis-Paul & Ebouele, Sergio Ewane, 2020. "Sampling a two dimensional matrix," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:csdana:v:149:y:2020:i:c:s0167947320300621
    DOI: 10.1016/j.csda.2020.106971
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    References listed on IDEAS

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    4. 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.
    5. Giovanni Strona & Domenico Nappo & Francesco Boccacci & Simone Fattorini & Jesus San-Miguel-Ayanz, 2014. "A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals," Nature Communications, Nature, vol. 5(1), pages 1-9, September.
    6. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
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    1. Rivest, Louis-Paul, 2021. "Limiting properties of an equiprobable sampling scheme for 0–1 matrices," Statistics & Probability Letters, Elsevier, vol. 172(C).

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