Abstract
The identification of the location of global extremes has received much attention in the literature on nonparametric regression. However, all proposed estimates and confidence regions seem to require that the true unknown function has a unique global maximum. In cases where the estimated function has various peaks of similar altitude, this assumption is hard to justify. Even if the true function attains its global maximum at a single point, the task remains to decide to which of the peaks of the estimated function this point corresponds. For this purpose we derive (not necessarily connected) confidence sets for the set of global maximizers based on multiple comparison procedures in connection with nonparametric curve estimates.
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