Abstract Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If n denotes the fixed sample size, the n units are drawn independently with probabilities that may vary from unit to unit and the samples in which all units are not distinct are rejected. More generally, in rejective sampling, we select repeated samples according to a basic sampling design until a selected sample meets a specified balancing tolerance. Given a set of auxiliary variables, we consider a procedure in which the probability sample is rejected unless the sample mean of the auxiliary variables is within a specified distance of its corresponding population mean. The procedure represents an alternative to the well-known balanced cube method. In this article, we propose an estimator of the variance under the rejective sampling design. We also present the results of a Monte Carlo simulation study.

中文翻译：

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排斥采样中总体均值方差估计程序

摘要拒绝采样是哈耶克（Hájek）于1964年首次提出的，它是一种选择唯一包含不同单位的样本的方法。如果n表示固定样本大小，则以可能随单位变化的概率独立绘制n个单位，并且拒绝所有单位都不相同的样本。更一般而言，在拒收采样中，我们根据基本采样设计选择重复的采样，直到选定的采样满足指定的平衡公差为止。给定一组辅助变量，我们考虑一个过程，其中概率样本将被拒绝，除非辅助变量的样本均值在其相应总体均值的指定距离内。该过程代表了众所周知的平衡立方体方法的替代方法。在这篇文章中，我们提出了拒绝抽样设计下的方差估计量。我们还介绍了蒙特卡洛模拟研究的结果。