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Sharp linear and block shrinkage wavelet estimation

✍ Scribed by Sam Efromovich

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 177 KB
Volume: 49
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(00)00064-x

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✦ Synopsis

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 deÿciency 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.

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