Inverse set estimation and inversion of simultaneous confidence intervals
受气候学和医学风险评估问题启发，提出一种通过反演同时置信区间来估计函数定义域中集合的方法，适用于密集和非密集域，并控制探索性数据分析中的第一类错误膨胀。
Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and coronavirus disease 2019 on hospitalized patients), we address the problem of estimating the set in the domain of a function whose image equals a predefined subset of the real line. Existing methods require strict assumptions. We generalize the estimation of such sets to dense and nondense domains with protection against inflated Type I error in exploratory data analysis. This is achieved by proving that confidence sets of multiple upper, lower, or interval sets can be simultaneously constructed with the desired confidence nonasymptotically through inverting simultaneous confidence intervals. Nonparametric bootstrap algorithm and code are provided.