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Sharp linear and block shrinkage wavelet estimation

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  • Efromovich, Sam

Abstract

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.

Suggested Citation

  • Efromovich, Sam, 2000. "Sharp linear and block shrinkage wavelet estimation," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 323-329, October.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:4:p:323-329
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    Cited by:

    1. Sam Efromovich & Zibonele Valdez-Jasso, 2010. "Aggregated wavelet estimation and its application to ultra-fast fMRI," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 841-857.

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