  Adaptive confidence balls are constructed for individual resolution levels as
well as the entire mean vector in a multiresolution framework. Finite sample
lower bounds are given for the minimum expected squared radius for confidence
balls with a prespecified confidence level. The confidence balls are centered
on adaptive estimators based on special local block thresholding rules. The
radius is derived from an analysis of the loss of this adaptive estimator. In
addition adaptive honest confidence balls are constructed which have guaranteed
coverage probability over all of $\mathbb{R}^N$ and expected squared radius
adapting over a maximum range of Besov bodies.
