We propose two methods to approximate the distribution function of a Studentized linear combination of order statistics for a simple random sample drawn without replacement from a finite population. Using auxiliary data available for the population units, the first method modifies a nonparametric bootstrap approximation, and the second one corrects an empirical saddlepoint approximation based on the bootstrap. We conclude from simulations that, on the tails of distribution of interest, both approximations improve their initial versions and alternative Edgeworth approximations.

中文翻译：

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有限总体 L 统计量的校准自举和鞍点近似

我们提出了两种方法来近似用于从有限总体中抽取而无需替换的简单随机样本的顺序统计的学生化线性组合的分布函数。使用可用于总体单位的辅助数据，第一种方法修改非参数自举近似，第二种方法基于自举修正经验鞍点近似。我们从模拟中得出结论，在兴趣分布的尾部，这两种近似都改进了它们的初始版本和替代 Edgeworth 近似。