ABSTRACT A short Edgeworth expansion is approximated for the distribution function of a Studentized linear combination of order statistics computed on a random sample drawn without replacement from a finite population, and using auxiliary data available for the population units. Simulations show an improvement over the usual Gaussian approximation and previous empirical Edgeworth expansions. Naive synthetic estimates of the distribution function, based on the auxiliary data only, yield accurate results when the auxiliary variable is well correlated with the study variable.

中文翻译：

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有限总体 L 统计量的校准 Edgeworth 扩展

摘要 一个简短的 Edgeworth 展开近似于一个学生化线性组合的分布函数，该组合是在从有限总体中抽取的随机样本上计算的，并且使用总体单元可用的辅助数据。模拟显示比通常的高斯近似和以前的经验 Edgeworth 扩展有所改进。当辅助变量与研究变量相关性良好时，分布函数的朴素综合估计仅基于辅助数据会产生准确的结果。