Confidence bands in density estimation
Confidence bands in density estimation
Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a fixed but arbitrary integer. The exceptional ("nongeneric") set of densities for which our results …