  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.
