Confidence intervals for nonparametric regression
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We demonstrate and discuss nonasymptotic bounds in probability for the cost of a regression scheme with a general loss function from the perspective of the Rademacher theory, and for the optimality with respect to the average L^2-distance to the underlying conditional expectations of least squares regression outcomes from the perspective of the Vapnik-Chervonenkis theory. The results follow from an analysis involving independent but possibly nonstationary training samples and can be extended, in a manner that we explain and illustrate, to relevant cases in which the training sample exhibits dependence.
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