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.

中文翻译：

---

对二维矩阵进行采样

摘要 提出了一种新的抽样设计，其单位可以排列为N×M矩阵。样本必须满足一些约束：行和列样本大小是预先设置的。所提出的抽样方法对满足约束条件的所有样本矩阵给出相同的选择概率。提出了三种在可行集中均匀选择样本的算法：基于多元超几何分布的精确算法、MCMC 算法和立方体方法。它们的性能使用蒙特卡罗模拟进行评估。对给定行或给定列中的抽样元素的设计进行了研究，并评估了建议设计下的单一包含和联合选择概率。为调查变量 y 的总体均值的 Horvitz-Thompson 估计量提出了几个方差估计量，并在 Monte Carlo 研究中比较了它们的性能。提供了一个数值示例，用于处理在 36 天内在 9 个地点发现的渔民的筒架调查。