Universal confidence sets for the mode of a regression function

We consider the problem of mode estimation in a random design regression model. Confidence sets for the modes can be derived as suitable neighbourhoods for maximum points of a regression estimator. For each sample size n, the neighbourhoods are chosen in such a way that they cover the true modes at least with a prescribed probability. The approach relies on concentration‐of‐measure inequalities for the regression estimators. The aim of the paper is to derive appropriate assertions for the Nadaraya–Watson estimator and to show how these results can be used for the derivation of universal confidence sets.