Universal confidence sets for the mode of a regression function
We consider the problem of mode estimation of the regression model with random (stochastic) design. Confidence sets for the modes can be derived as suitable neighborhoods of maximum point of a regression estimator. For each sample size n the neighborhoods are chosen in such a way that they cover the true modes at least with a prescribed probability. The approach relies on concentration-on-measure inequalities for the regression estimators. The aim of the talk is to derive appropriate assertions for the famous regression estimators and to show how they can be used for the determination of universal confidence sets.
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