不平衡样本中监测与筛选的自适应阈值：最优性与敏感性提升
Adaptive Thresholds for Monitoring and Screening in Imbalanced Samples: Optimality and Boosting Sensitivity
AI总结：
针对不平衡样本，提出依赖协变量的自适应阈值以提升稀有类别敏感性，给出最优阈值函数及可行计算程序，并验证其有效性。
摘要：
假设对（标准化）测量值或统计量进行监测，当超过阈值时发出警报。通常，潜在总体在重要的离散变量方面是异质的，因此样本可能由不平衡的类别组成。我们提出使用依赖于这些协变量的阈值，以提升稀有类别的敏感性，否则这些类别往往会被忽略。在温和条件下，我们确定了最优阈值函数，并开发了一种可行的计算程序。此外，对于比例规则，我们提出了阈值函数的非参数估计器，并证明了中心极限定理，包括用于标准化的条件均值和方差被估计的情况。为了可行的不确定性量化，我们提出了一种自助法方案。该方法通过真实数据分析进行了说明和评估。
英文摘要：
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of imbalanced classes. We propose to use thresholds which depend on such covariates to boost the sensitivity for rare classes, which otherwise tend to be ignored. Under mild conditions, we identify optimal threshold functions and develop a feasible procedure for their computation. Further, for the proportional rule a nonparametric estimator of the threshold function is proposed and a central limit theorem is shown, including the case that conditional mean and variance used for standardization are estimated. For feasible uncertainty quantification a bootstrap scheme is proposed. The approach is illustrated and evaluated by a real data analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
