Workshop on Structure Adapting Methods - Abstract

Nickl, Richard

Finite Sample Confidence Bands for Needlet Estimators on the Unit Sphere

(This is joint work with G.Kerkyacharian and D.Picard). We show how one can use the recently introduced needlet density estimators on the unit sphere to construct valid finite sample confidence bands. These bands are shown to adapt to the unknown Hoelder smoothness of the density under additional structural assumptions on the density $f$. This condition can be interpreted in terms of the attainment of the Hoelder exponents of $f$.