We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

中文翻译：

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具有辅助信息的基于设计的随机排列模型

我们扩展随机置换模型以获得有限总体均值的最佳线性无偏估计量，在无替换的简单随机抽样 (SRS) 或分层 SRS 下考虑辅助变量。所提出的方法为众所周知的结果提供了一种基于设计的系统性证明，这些结果涉及在不需要指定响应和辅助变量之间的函数关系的最小假设下得出的常见估计量。