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Motivated by the questions of risk assessment in climatology (temperaturechange in North America) and medicine (impact of statin usage and COVID-19 onhospitalized patients), we address the problem of estimating the set in thedomain of a function whose image equals a predefined subset. Existing methodsthat construct confidence sets require strict assumptions. We generalize theestimation of such sets to dense and non-dense domains with protection against"data peeking" by proving that confidence sets of multiple levels can besimultaneously constructed with the desired confidence non-asymptoticallythrough inverting simultaneous confidence bands. A non-parametric bootstrapalgorithm and code are provided.

Inverse set estimation and inversion of simultaneous confidence intervals