✦ LIBER ✦

On Minimax Wavelet Estimators

✍ Scribed by B. Delyon; A. Juditsky

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 283 KB
Volume: 3
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1996.0017

No coin nor oath required. For personal study only.

✦ Synopsis

In the paper minimax rates of convergence for wavelet estimators are studied. The estimators are based on the shrinkage of empirical coefficients βjk of wavelet decomposition of unknown function with thresholds λ j . These thresholds depend on the regularity of the function to be estimated. In the problem of density estimation and nonparametric regression we establish upper rates of convergence over a large range of functional classes and global error measures. The constructed estimate is minimax (up to constant) for all L π error measures, 0 < π ∞ simultaneously.

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