• Corpus ID: 15508105

Incorporating Information on Neighboring Coefficients Into Wavelet Estimation

@article{Cai2001IncorporatingIO,
  title={Incorporating Information on Neighboring Coefficients Into Wavelet Estimation},
  author={T. Tony Cai and Bernard W. Silverman},
  journal={Sankhya},
  year={2001},
  volume={63},
  pages={127}
}

• T. Cai, B. Silverman
• Published 2001
• Mathematics
• Sankhya

In standard wavelet methods, the empirical wavelet coe cients are thresholded term by term, on the basis of their individual magnitudes. Information on other coe cients has no in uence on the treatment of particular coe cients. We propose a wavelet shrinkage method that incorporates information on neighboring coe cients into the decision making. The coe cients are considered in overlapping blocks; the treatment of coe cients in the middle of each block depends on the data in the whole block. The asymptotic and numerical performances of two particular versions of the estimator are investigated. We show that, asymptotically, one version of the estimator achieves the exact optimal rates of convergence over a range of Besov classes for global estimation, and attains adaptive minimax rate for estimating functions at a point. In numerical comparisons with various methods, both versions of the estimator perform excellently.