Uncertainty quantification for robust variable selection and multiple testing

We study the problem of identifying set active variables, termed in literature as variable selection or multiple hypothesis testing, depending on pursued criteria. For a general robust setting non-normal, possibly dependent observations and generalized notion set, we propose procedure that is used simultaneously for both tasks, testing. The based risk hull minimization method, but can also be obtained result an empirical Bayes approach penalization strategy. address its quality via various criteria: Hamming risk, FDR, FPR, FWER, NDR, FNR, testing risks, e.g., MTR=FDR+NDR; discuss weak optimality our results. Finally, introduce study, first time, uncertainty quantification context setting.