Sharp linear and block shrinkage wavelet estimation

Sam Efromovich

Statistics & Probability Letters, 2000, vol. 49, issue 4, 323-329

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.

Keywords: Adaptation; Asymptotic; Exact; constant; Mean; integrated; squared; error; Nonparametric; estimation; Numerical; study (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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