Junting Ren, Fabian J E Telschow, Armin Schwartzman
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引用次数: 0
摘要
受气候学（北美气温变化）和医学（他汀类药物的使用和 2019 年冠状病毒疾病对住院病人的影响）中风险评估问题的启发，我们解决了估计函数域中的集合的问题，该函数的图像等于实线的预定义子集。现有方法需要严格的假设条件。我们将此类集合的估计方法推广到稠密域和非稠密域，并在探索性数据分析中防止 I 类错误的扩大。为此，我们证明了多个上集、下集或区间集的置信度集可以通过同时倒置置信区间，以非渐近的方式同时构建出所需的置信度。提供了非参数引导算法和代码。
Inverse set estimation and inversion of simultaneous confidence intervals.
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.
期刊介绍：
The Journal of the Royal Statistical Society, Series C (Applied Statistics) is a journal of international repute for statisticians both inside and outside the academic world. The journal is concerned with papers which deal with novel solutions to real life statistical problems by adapting or developing methodology, or by demonstrating the proper application of new or existing statistical methods to them. At their heart therefore the papers in the journal are motivated by examples and statistical data of all kinds. The subject-matter covers the whole range of inter-disciplinary fields, e.g. applications in agriculture, genetics, industry, medicine and the physical sciences, and papers on design issues (e.g. in relation to experiments, surveys or observational studies).
A deep understanding of statistical methodology is not necessary to appreciate the content. Although papers describing developments in statistical computing driven by practical examples are within its scope, the journal is not concerned with simply numerical illustrations or simulation studies. The emphasis of Series C is on case-studies of statistical analyses in practice.
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