Sharp linear and block shrinkage wavelet estimation

The results of Hall et al. (1998, Ann. Statist. 26, 922-943) together with Efromovich (2000, Bernoulli) imply that a data-driven block shrinkage wavelet estimator, which mimics a sharp minimax linear oracle, is rate optimal over spatially inhomogeneous function spaces. This result does not contradict to known theoretical results about the rate deficiency of linear estimates; instead, it tells us that adaptive estimates that mimic an optimal linear oracle may be possible alternatives to threshold-adaptive wavelet estimates. New results on sharp minimax linear estimation over Besov spaces and data-driven block shrinkage estimation for small sample sizes are presented that further develop the "linear" branch of the wavelet estimation theory.