On the block thresholding wavelet estimators with censored data

Journal of Multivariate Analysis

Volumn 99, Issue 8, 2008, Pages 1518-1543

  Li, Linyuan ^a  

^a UNIVERSITY OF NEW HAMPSHIRE   (United States)

Author keywords

Adaptive estimation; Besov spaces; Block thresholding; Censored data; Density estimation; Minimax estimation; Nonlinear wavelet based estimator; Rates of convergence

Indexed keywords

EID: 48549104300     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2008.01.001     Document Type: Article

References (24)

1. Antoniadis A., Grégoire G., and Nason G. Density and hazard rate estimation for right-censored data by using wavelet methods. J. Roy. Statist. Soc. B 61 (1999) 63-84
2. Cai T. Adaptive wavelet estimation: A block thresholding and oracle inequality approach. Ann. Statist. 27 (1999) 898-924
3. Cai T. On block thresholding in wavelet regression: Adaptivity, block size, and threshold level. Statistic Sinica 12 (2002) 1241-1273
4. Chicken E., and Cai T. Block thresholding for density estimation: Local and global adaptivity. J. Multivariate Anal. 95 (2005) 76-106
5. Cohen A., Daubechies I., and Vial P. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harm. Anal. 1 (1993) 54-82
6. Daubechies I. Ten Lectures on Wavelets (1992), SIAM, Philadelphia
7. Donoho D.L., and Johnstone I.M. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 (1994) 425-455
8. Donoho D.L., and Johnstone I.M. Adapting to unknown smoothness via wavelet shrinking. J. Am. Statist. Assoc. 90 (1995) 1200-1224
9. Donoho D.L., and Johnstone I.M. Minimax estimation via wavelet shrinkage. Ann. Statist. 26 (1998) 879-921
10. Donoho D.L., Johnstone I.M., Kerkyacharian G., and Picard D. Wavelet shrinkage: asymptopia? (with discussion). J. Roy. Statist. Soc. B 57 (1995) 301-369
11. Donoho D.L., Johnstone I.M., Kerkyacharian G., and Picard D. Density estimation by wavelet thresholding. Ann. Statist. 24 (1996) 508-539
12. Fan J., and Gijbels I. Censored regression: Local linear approximations and their applications. J. Am. Statist. Assoc. 89 (1994) 560-570
13. Hall P., Kerkyacharian G., and Picard D. Block threshold rules for curve estimation using kernel and wavelet method. Ann. Statist. 26 (1998) 922-942
14. Hall P., Kerkyacharian G., and Picard D. On the minimax optimality of block thresholded wavelet estimators. Statistica Sinica 9 (1999) 33-50
15. Härdle W., Kerkyacharian G., Picard D., and Tsybakov A. Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics vol. 129 (1998)
16. Li L. Non-linear wavelet-based density estimators under random censorship. J. Statist. Planning Inference 117 (2003) 35-58
17. Li L. On the minimax optimality of wavelet estimators with censored data. J. Statist. Planning Inference 137 (2007) 1138-1150
18. Marron J.S., and Padgett W.J. Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples. Ann. Statist. 15 (1987) 1520-1535
19. Meyer Y. Wavelets and Operators (1992), Cambridge University Press, Cambridge
20. Nason G.P. Wavelet shrinkage using cross-validation. J. Roy. Statist. Soc. B 58 (1996) 463-479
21. Stute W. The central limit theorem under random censorship. Ann. Statist. 23 (1995) 422-439
22. Triebel H. Theory of Function Spaces II (1992), Birkhäuser, Basel
23. Vidakovic B. Statistical Modeling by Wavelets (1999), John Wiley & Sons, Inc.
24. Talagrand M. Sharper bounds for Gaussian and empirical processes. Ann. Probab. 22 1 (1994) 28-76