Estimation of the conditional distribution in a conditional Koziol-Green model

Test

Volumn 9, Issue 1, 2000, Pages 97-122

  Veraverbeke, Noel ^a   Cadarso Suárez, Carmen ^b  

^a HASSELT UNIVERSITY   (Belgium)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Asymptotic normality; Consistency; Proportional hazard; Regression; Right censoring

Indexed keywords

EID: 0011092194     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02595853     Document Type: Article

References (31)

1. Abdushukurov, A.A. (1984). On some estimates of the distribution function under random censorship. In Conference of Young Scientists, Mathematical Institute of the Academic Sciences, Uzbek SSR, Tashkent. VINITI No. 8756-V (in Russian).
2. Aerts, M., P. Janssen and N. Veraverbeke (1994). Asymptotic theory for regression quantile estimators in the heteroscedastic regression model. In Asymptotic Statistics (P. Mandl and M. Husková ed.) Physica-Verlag, Heidelberg, 151-161.
3. Beran, R. (1981). Nonparametric regression with randomly censored survival data. Technical Report, University of California, Berkeley.
4. Cheng, P.E. and G.D. Lin (1984). Maximum likelihood estimation of survival function under the Koziol-Green proportional hazards model. Technical Report B-84-5, Institute of Statistics, Academia Sinica, Taipei, Taiwan.
5. Cheng, P.E. and G.D. Lin (1987). Maximum likelihood estimation of a survival function under the Koziol-Green proportional hazards model. Statistics and Probability Letters, 5, 75-80.
6. Csörgo, S. (1988). Estimation in the proportional hazards model of random censorship. Statistics, 19, 437-463.
7. Csörgo, S. and J. Mielniczuk (1988). Density estimation in the simple proportional hazards model. Statistics and Probability Letters, 6, 419-426.
8. Dabrowska, D.M. (1987). Non-parametric regression with censored survival data. Scandinavian Journal of Statistics, 14, 181-197.
9. Dabrowska, D.M. (1989). Uniform consistency of the kernel conditional Kaplan-Meier estimate. Annals of Statistics, 17, 1157-1167.
10. Dabrowska, D.M. (1992a). Variable bandwidth conditional Kaplan-Meier estimate. Scandinavian Journal of Statistics, 19, 351-361.
11. Dabrowska, D.M. (1992b). Nonparametric quantile regression with censored data. Sankhya, A, 54, 252-259.
12. 1-Statistical Procedures and Related Topics (Y. Dodge ed.) IMS Lecture Notes Monograph Series, vol. 31, Hayward, California, 385-398.
13. Fleming, T.R. and D.P. Harrington (1991). Counting Processes and Survival Analysis. Wiley-Interscience.
14. Földes, A. and L. Rejto (1981). A LIL type result for the product limit estimator. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 56, 75-86.
15. Gasser, T. and H.G. Müller (1984). Estimating regression functions and their derivatives by the kernel method. Scandinavian Journal of Statistics, 11, 171-185.
16. Gentleman, R. and J. Crowley (1991). Graphical models for censored data. Journal of the American Statistical Association, 86, 678-683.
17. Georgiev, A.A. (1989). Asymptotic properties of the multivariate Nadaraya-Watson regression function estimate: the fixed design case. Statistics and Probability Letters, 7, 35-40.
18. Ghorai, J.K. and L.M. Pattanaik (1993). Asymptotically optimal bandwidth selection of the kernel density estimator under the proportional hazards model. Communications in Statistics-Theory and Methods, 22, 1383-1401.
19. Gijbels, I. and V.K. Klonias (1981). Density estimation under the Koziol-Green model of censoring by penalized likelihood methods. Canadian Journal of Statistics, 19, 23-38.
20. Gijbels, I. and N. Veraverbeke (1989). Quantile estimation in the proportional hazards model of random censorship. Communications in Statistics-Theory and Methods, 18, 1645-1663.
21. González-Manteiga, W. and C. Cadarso-Suárez (1991). Linear regression with randomly right-censored data using prior nonparametric estimation. In Nonparametric Functional Estimation and Related Topics (G. Roussas ed.) Kluwer Academic Press, 315-328.
22. González-Manteiga, W. and C. Cadarso-Suárez (1994). Asymptotic properties of a generalized Kaplan-Meier estimator with some applications. Journal of Nonparametric Statistics, 4, 65-78.
23. Henze, N. (1993). A quick omnibus test for the proportional hazards model of random Censorship. Statistics, 24, 253-263.
24. Herbst, T. (1992). Test of fit with the Koziol-Green model for random censorship. Statistics and Decisions, 10, 163-171.
25. Koziol, J.A. and S.B. Green (1976). A Cramér-von Mises statistic for randomly censored data. Biometrika, 63, 465-474.
26. Lo, S.-H. and K. Singh (1986). The product-limit estimator and the bootstrap: some asymptotic representations. Probability Theory and Related Fields, 71, 455-465.
27. Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
28. Van Keilegom, I. and N. Veraverbeke (1996). Uniform strong convergence results for the conditional Kaplan-Meier estimator and its quantiles. Communications in Statistics-Theory and Methods, 25, 2251-2265.
29. Van Keilegom, I. and N. Veraverbeke (1997). Estimation and bootstrap with censored data in fixed design nonparametric regression. Annals of the Institute of Statistical Mathematics, 49, 467-491.
30. Van Keilegom, I. and N. Veraverbeke (1998). Bootstrapping quantiles in a fixed design regression model with censored data. Journal of Statistical Planning and Inference, 69, 115-131.
31. Veraverbeke, N. (1994). Bootstrapping quantiles in the proportional hazards model of random censorship. Communications in Statistics-Theory and Methods, 23, 997-1007.