  A theory of superefficiency and adaptation is developed under flexible
performance measures which give a multiresolution view of risk and bridge the
gap between pointwise and global estimation. This theory provides a useful
benchmark for the evaluation of spatially adaptive estimators and shows that
the possible degree of superefficiency for minimax rate optimal estimators
critically depends on the size of the neighborhood over which the risk is
measured. Wavelet procedures are given which adapt rate optimally for given
shrinking neighborhoods including the extreme cases of mean squared error at a
point and mean integrated squared error over the whole interval. These adaptive
procedures are based on a new wavelet block thresholding scheme which combines
both the commonly used horizontal blocking of wavelet coefficients (at the same
resolution level) and vertical blocking of coefficients (across different
resolution levels).
