Paper detail

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 &#34;generic&#34; subset of the union of $t$-Hölder balls, $0<t\le r$, where $r$ is a fixed but arbitrary integer. The exceptional (&#34;nongeneric&#34;) set of densities for which our results do not hold is shown to be nowhere dense in the relevant Hölder-norm topologies. In the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density estimators, which are of independent interest.