Abstract

Identifying the level set of a regression function, {x: m(x)>c}, is a fundamental problem in nonparametric statistics. We develop a methodology that estimates this set while controlling FDR asymptotically. To handle the continuous nature of X, we consider a continuous version of FDR, which evaluates the proportion of the falsely discovered region with respect to a given measure μ. We address two settings: (i) when μ is known (e.g., Lebesgue), and (ii) when μ is the unknown probability measure of X. For each case, we provide a multiple testing procedure with theoretical guarantees. The effectiveness of our approach is validated through simulations and an application to crop yield data.