Understanding WaveShrink: Variance and bias estimation

Biometrika

Volumn 83, Issue 4, 1996, Pages 727-745

  Bruce, Andrew G ^a   Gao, Hong Y E ^a  

^a Parametric Technology Corporation   (United States)

Author keywords

Bias and variance estimation; Confidence interval; Function estimation; Hard shrinkage; Minimax estimation; Nonparametric regression; Soft Shrinkage; Threshold selection; Wavelet transform; WaveShrink

Indexed keywords

EID: 0000835306     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/83.4.727     Document Type: Article

References (17)

1. BICKEL, P. J. (1981). Minimax estimation of the mean of a normal distribution when the parameter space is restricted. Ann. Statist. 9, 1301-9.
2. BICKEL, P. J. (1983). Minimax estimation of a normal mean subject to doing well at a point. In Recent Advances in Statistics, Ed. M. H. Rizui, J. S. Rustagi and D. Siegmund, pp. 511-28. New York: Academic Press.
3. BREIMAN, L. (1985). Better subset regression using the nonnegative garrote. Technometrics 37, 373-84.
4. BRILLINGER, D. R. (1994a). Some river wavelets. Environmetrics 5, 211-20.
5. BRILLINGER, D. R. (1994b). Uses of cumulants in wavelet analysis. In Advanced Signal Processing: Algorithms, Architectures, and Implementations, 2296, Ed. F. T. Luk, pp. 2-18. San Diego, CA: Int. Soc. Optic. Eng.
6. BRILLINGER, D. R. (1995). Some uses of cumulants in wavelet analysis. J. Nonparam. Statist. 6, 93-114.
7. BRUCE, A. G. & GAO, H.-Y. (1994). S + WAVELETS User's Manual. 1700 Westlake Ave. N, Seattle, WA 98109-9891; StatSci Div., MathSoft, Inc.
8. BRUCE, A. G. & GAO, H.-Y. (1995). WaveShrink: Shrinkage functions and thresholds. In Wavelet Applications in Signal and Image Processing III, 2569, Ed. A. F. Laine and M. A. Unser, pp. 270-83. San Diego, CA: Int. Soc. Optic. Eng.
9. COHEN, A., DAUBECHIES, I. & VIAL, P. (1993). Wavelets on the interval and fast wavelet transforms. Appl. Computat. Harmon. Anal. 1, 54-81.
10. DAUBECHIES, I. (1992). Ten Lectures on Wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics.
11. DENNIS, J. E. & MEI, H. H. W. (1979). Two new unconstrained optimization algorithms which use function and gradient values. J. Optimiz. Theory Applic. 28, 453-83.
12. DONOHO, D., JOHNSTONE, I., KERKYACHARIAN, G. & PICARD, D. (1995). Wavelet shrinkage: Asymptopia? (with Discussion). J. R. Statist. Soc. B 57, 301-69.
13. DONOHO, D. L. & JOHNSTONE, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425-55.
14. DONOHO, D. L. & JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Assoc. 90, 1200-24.
15. MALLAT, S. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Patt. Anal Mach. Intell. 11, 674-93.
16. MARRON, J. S. (1995). Discussion of paper by D. Donoho et al. J. R. Statist. Soc. B 57, 338-9.
17. STATSCI (1993). S-PLUS User's Manual, Version 3.2. 1700 Westlake Ave., Suite 500, Seattle, WA 98109-9891: StatSci Div., MathSoft, Inc.