Asymptotic minimaxity of wavelet estimators with sampled data

Statistica Sinica

Volumn 9, Issue 1, 1999, Pages 1-32

  Donoho, David L ^a   Johnstone, Iain M ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Besov spaces; Bounded operators between besov spaces; Minimax estimation; Thresholding; Wavelet transforms of sampled data; Wavelets; White noise equivalence

Indexed keywords

EID: 0033466896     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Brown, L. D. and Low, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 3, 2384-2398.
2. Cohen, A., Daubechies, I., Jawerth, B. and Vial, P. (1993). Multiresolution analysis, wavelets, and fast algorithms on an interval. Comptes Rendus Acad. Sci. Paris (A) 316, 417-421.
3. Delyon, B. and Juditsky, A. (1996). On minimax wavelet estimators. Applied Computational and Harmonic Analysis 3, 215-228.
4. Deslauriers, G. and Dubuc, S. (1987). Interpolation dyadique. In Fractals, Dimensions non-entières et applications. Masson, Paris.
5. Deslauriers, G. and Dubuc, S. (1989). Symmetric iterative interpolation processes. Constr. Approx. 5, 49-68.
6. DeVore, R. and Lorentz, G. (1993). Constructive Approximation. Springer Verlag, New York.
7. Donoho, D. (1992a). De-noising via soft-thresholding. IEEE Trans. Inform. Theory 41, 613-627.
8. Donoho, D. (1992b). Interpolating wavelet transforms. Technical Report 408, Department of Statistics, Stanford University.
9. Donoho, D. (1993). Smooth wavelet decompositions with blocky coefficient kernels. In Recent Advances in Wavelet Analysis (Edited by L. Schumaker). Academic Press, Boston.
10. Donoho, D. (1994). Asymptotic minimax risk for sup-norm loss; solution via optimal recovery. Probab. Theory Related Fields 99, 145-170.
11. Donoho, D. (1995). Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Applied Computational and Harmonic Analysis 2, 101-126.
12. Donoho, D. L. and Johnstone, I. M. (1990). Wavelets and optimal nonparametric function estimation. Technical Report, Department of Statistics, University of California Berkeley.
13. Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425-455.
14. Donoho, D. L. and Johnstone, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26, 879-921.
15. Donoho, D. L., Johnstone, I. M., Kerkyacharian, G. and Picard, D. (1995). Wavelet shrinkage: Asymptopia? (With Discussion). J. Roy. Statist. Soc. Ser. B 57, 301-369.
16. Donoho, D. L., Liu, R. C. and MacGibbon, K. B. (1990). Minimax risk over hyperrectangles, and implications. Ann. Statist. 18, 1416-1437.
17. Donoho, D. L. and Nussbaum, M. (1990). Minimax quadratic estimation of a quadratic functional. J. Complexity 6, 290-323.
18. Dubuc, S. (1986). Interpolation through an iterative scheme. J. Math. Anal. Appl. 114, 185-204.
19. Frazier, M., Jawerth, B. and Weiss, G. (1991). Littlewood-Paley Theory and the study of function spaces. NSF-CBMS Regional Conf. Ser in Mathematics, 79, American Mathematical Society, Providence, RI.
20. Meyer, Y. (1990). Ondelettes et Opérateurs, I: Ondelettes, II: Opérateurs de Calderón-Zygmund, III: (with R. Coifman), Opérateurs multilinéaires. Hermann, Paris. English translation of first volume is published by Cambridge University Press.
21. Peetre, J. (1975). New Thoughts on Besov Spaces. I. Duke University Mathematics Series, Raleigh, Durham.
22. Triebel, H. (1992). Theory of Function Spaces II. Birkhäuser Verlag, Basel.