Empirical Bernstein confidence intervals for kernel smoothers attain nominal coverage up to a remainder of order n to the minus 2S over 2S+1 while achieving minimax optimal widths under S-th order local smoothness.
Journal of Multivariate Analysis , volume=
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Empirical Bernstein Confidence Intervals for Kernel Smoothers: A Safe and Sharp Way to Exhaust Assumed Smoothness
Empirical Bernstein confidence intervals for kernel smoothers attain nominal coverage up to a remainder of order n to the minus 2S over 2S+1 while achieving minimax optimal widths under S-th order local smoothness.