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Anti-Concentration and Honest Adaptive Confidence Bands
Anti-Concentration Honest Adaptive Confidence Bands
2013/4/28
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the Smirnov-Bickel-Rosenblatt (SBR) condition; see e.g. Gine and Nickl (2010). This co...
Adaptive confidence bands in the nonparametric fixed design regression model
Adaptive confidence bands nonparametric fixed design regression model
2012/9/19
In this note, we consider the problem of existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl [10] to the present case. In the course of th...
We show that there do not exist adaptive confidence bands for
curve estimation except under very restrictive assumptions. We propose
instead to construct adaptive bands that cover a surrogate functi...