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Limiting properties of an equiprobable sampling scheme for 0–1 matrices

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  • Rivest, Louis-Paul

Abstract

A sampling scheme that selects a random 0–1 matrix of size N×M uniformly in the set of 0–1 matrices with predetermined row and column totals is investigated. The limits, as M goes to ∞ and N is fixed, of the column relative frequencies is derived. The limiting values give a sampling design for a population of N units that generalizes the conditional Poisson sampling design introduced by Hajek. A method to calculate the joint selection probabilities for this new design using the known single inclusion probabilities is presented. Numerical examples show that the limiting theorem provides good approximations to the fixed M column probabilities of a random matrix.

Suggested Citation

  • Rivest, Louis-Paul, 2021. "Limiting properties of an equiprobable sampling scheme for 0–1 matrices," Statistics & Probability Letters, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:stapro:v:172:y:2021:i:c:s0167715221000092
    DOI: 10.1016/j.spl.2021.109047
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    References listed on IDEAS

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    1. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
    2. Louis-Paul Rivest & Sophie Baillargeon, 2007. "Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population," Biometrics, The International Biometric Society, vol. 63(4), pages 999-1006, December.
    3. Rivest, Louis-Paul & Ebouele, Sergio Ewane, 2020. "Sampling a two dimensional matrix," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
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    Cited by:

    1. Louis‐Paul Rivest & Serigne Abib Gaye, 2023. "Using Survey Sampling Algorithms For Exact Inference in Logistic Regression," International Statistical Review, International Statistical Institute, vol. 91(1), pages 18-34, April.

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