  A data-driven block thresholding procedure for wavelet regression is proposed
and its theoretical and numerical properties are investigated. The procedure
empirically chooses the block size and threshold level at each resolution level
by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive
over a class of Besov bodies and achieves simultaneously within a small
constant factor of the minimax risk over a wide collection of Besov Bodies
including both the ``dense'' and ``sparse'' cases. The procedure is easy to
implement. Numerical results show that it has superior finite sample
performance in comparison to the other leading wavelet thresholding estimators.
