Inverse set estimation and inversion of simultaneous confidence intervals
Methodology
2025-04-29 v3 Statistics Theory
Statistics Theory
Abstract
Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a function whose image equals a predefined subset. Existing methods that construct confidence sets require strict assumptions. We generalize the estimation of such sets to dense and non-dense domains with protection against "data peeking" by proving that confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically through inverting simultaneous confidence bands. A non-parametric bootstrap algorithm and code are provided.
Cite
@article{arxiv.2210.03933,
title = {Inverse set estimation and inversion of simultaneous confidence intervals},
author = {Junting Ren and Fabian J. E. Telschow and Armin Schwartzman},
journal= {arXiv preprint arXiv:2210.03933},
year = {2025}
}