Adaptive estimation of hazard rate with censored data

Communications in Statistics - Theory and Methods

Volumn 37, Issue 8, 2008, Pages 1284-1305

  Brunel, Elodie ^a   Comte, Fabienne ^b  

^a UNIV MONTPELLIER   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Adaptive estimation; Hazard rate; Minimax rate; Nonparametric penalized contrast estimator

Indexed keywords

ADAPTIVE SYSTEMS; DATA REDUCTION; FUNCTION EVALUATION; PARAMETER ESTIMATION; RANDOM PROCESSES;

ADAPTIVE ESTIMATION; DATA-DRIVEN RANDOM PENALTY FUNCTION; HAZARD RATE; MINIMAX RATE; NONPARAMETRIC PENALIZED CONTRAST ESTIMATORS;

POLYNOMIAL APPROXIMATION;

EID: 39449103545     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920701713302     Document Type: Article

References (31)

1. Antoniadis, A., Grégoire, G. (1990). Penalized likelihood estimation for rates with censored survival data. Scand. J. Statist. 17:43-63.
2. Antoniadis, A., Grégoire, G., Nason, G. (1999). Density and hazard rate estimation for right-censored data by using wavelet methods. J. R. Stat. Soc., Series B Stat. Methodol. 61:63-84.
3. Baraud, Y., Comte, F., Viennet, G. (2001). Model selection for (auto)-regression with dependent data. ESAIM Probab. Statist. 5:33-49.
4. Barron, A. R., Birgé, L., Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113:301-413.
5. Barron, A. R., Cover, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37:1034-1054.
6. Birgé, L., Massart, P. (1997). From model selection to adaptive estimation. In: Pollard, D., Torgersen, E. Yang, G. eds. Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics. New-York: Springer-Verlag, pp. 55-87.
7. Birgé, L., Massart, P. (2000). An adaptive compression algorithm in Besov spaces. Constr. Approx. 16:1-36.
8. Brunel, E., Comte, F. (2004). Adaptive estimation of hazard rate with censored data. Preprint MAP5 2004-16, http://www.math-info.univ-paris5.fr/map5/ publis/abstracts04.html.
9. Comte, F., Rozenholc, Y. (2002). Adaptive estimation of mean and volatility functions in (auto-)regressive models. Stoch. Proc. Appl. 97:111-145.
10. Comte, F., Rozenholc, Y. (2004). A new algorithm for fixed design regression and denoising. Ann. Inst. Statist. Math. 56:449-473.
11. Dabrowska, D. M. (1987). Nonparametric regression with censored survival time data. Scand. J. Statist. 14:181-197.
12. Dabrowska, D. M., Duffy, D. L., Zhang, Z. D. (1999). Hazard and density estimation from bivariate censored data. J. Nonparametr. Statist. 10:67-93.
13. Delecroix, M., Yazourh, Y. (1991). Nonparametric inference for failure rates with random right censorship: the method of orthogonal functions [French]. Statist. Anal. Données 16(3): 39-62.
14. DeVore, R. A., Lorentz, G. G. (1993). Constructive Approximation. New york: Springer-Verlag.
15. Döhler, S., Rüschendorf, L. (2002). Adaptive estimation of hazard functions. Probab. Math. Statist. 22(2):355-379.
16. Donoho, D. L., Johnstone, I. M. (1998). Minimax estimation with wavelet shrinkage. Ann. Statist. 26:879-921.
17. Efromovich, S. (1999). Nonparametric Curve Estimation: Methods, Theory and Applications. New York: Springer-Verlag.
18. Efromovich, S. (2001). Density estimation under random censorship and order restrictions: from asymptotic to small sample sizes. J. Amer. Statist. Assoc. 96:667-685.
19. Huber, C., MacGibbon, B. (2004). Lower bounds for estimating a hazard. Advances in Survival Analysis. Amsterdam: Elsevier, pp. 209-226
20. Kaplan, E. L., Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53:457-481.
21. 2 rate of convergence for hazard regression. Scand. J. Statist. 22:143-157.
22. Lo, S. H., Mack, Y. P., Wang, J. L. (1989). Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator. Probab. Theory Related Fields 80:461-473.
23. Marron, J., Padgett, W. J. (1987). Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples. Ann. Statist. 15:1520-1535.
24. Massart, P. (1990). The tight constant in Dvoretzky-Kiefer-Wolfowitz inequality. Ann. Probab. 18:1269-1283.
25. Mielniczuk, J. (1985). Properties of some kernel estimators and of the adapted Loftsgarden-Quesenberry estimator of a density function for censored data. Period. Math. Hungar. 16:69-81.
26. Patil, P. (1997). Nonparametric hazard rate estimation by orthogonal wavelet method. J. Statist. Plann. Inference 60:153-168.
27. Reid, N. (1981). Influence functions for censored data. Ann. Statist. 9:78-92.
28. Reynaud-Bouret, P. (2006). Penalized projection estimators of the Aalen multiplicative intensity. Bernoulli 12:633-661.
29. Stute, W. (1995). The central limit theorem under random censorship. Ann. Statist. 23:422-439.
30. Talagrand, M. (1996). New concentration inequalities in product spaces. Invent. Math. 126:505-563.
31. Wu, S. S., Wells, M. T. (2003). Nonparametric estimation of hazard functions by wavelet methods. Nonparametric Statistics 15:187-203.