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

Louis-Paul Rivest

Statistics & Probability Letters, 2021, vol. 172, issue C

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.

Keywords: Conditional Poisson sampling; Entropy; Null model analysis; Occupancy data; Weak law of large number (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2021.109047

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