Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data

Journal of Multivariate Analysis

Volumn 69, Issue 2, 1999, Pages 155-166

  Wong, George Y C ^a   Yu, Qiqing ^a  

^a NONE

Author keywords

Asymptotic normality; Asymptotic variance; Consistent estimate; Generalized MLE; Multivariate interval censored data; Multivariate survival analysis

Indexed keywords

EID: 0001449575     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1998.1807     Document Type: Article

References (21)

1. G. Campbell, Nonparametric bivariate estimation with randomly censored data, Biometrika 68 (1981), 417-422.
2. M. N. Chang and G. Yang, Strong consistency of a self-consistent estimator of the survival function with doubly censored data, Ann. Statist. 15 (1987), 1536-1547.
3. D. G. Clayton, A model of association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika 65 (1978), 141-151.
4. D. G. Clayton and J. Cuzick, Multivariate generalizations of the proportional hazards model (with discussion), J. Roy. Statist. Soc. Ser. A 148 (1985), 82-117.
5. D. M. Dabrowska, Kaplan-Meier estimate on the plane, Ann. Statist. 16 (1988), 1475-1489.
6. R. Gill, Multivariate survival analysis, Theory Prob. Appl. 37 (1992), 18-31.
7. P. Groeneboom and J. A. Wellner, "Information Bounds and Nonparametric Maximum Likelihood Estimation," Birkhäuser, Basel, 1992.
8. M. G. Gu and C. H. Zhang, Asymptotic properties of self-consistent estimator based on doubly censored data, Ann. Statist. 21 (1993), 611-624.
9. J. A. Hanley and M. N. Parnes, Nonparametric estimation of a multivariate distribution in the presence of censoring, Biometrics 39 (1983), 129-139.
10. The Italian-American Cataract Study Group, Incidence and progression of cortical, nuclear, and posterior subcapsular cataracts, Amer. J. Ophthal. 118 (1994), 623-631.
11. E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481.
12. D. Y. Lin and Z. L. Ying, A simple nonparametric estimator of the bivariate survival function under univariate censoring, Biometrika 80 (1993), 573-581.
13. R. Peto, Experimental survival curves for interval-censored data, Appl. Statist. 22 (1973), 86-91.
14. R. L. Prentice and J. Cai, Covariance and survival function estimation using censored multivariate failure time data, Biometrika 79(3) (1992), 495-512.
15. S. O. Samuelsen and J. Kongerud, Interval censoring in longitudinal data of respiratory symptoms in aluminum potroom workers: A comparison of methods, Statist. Medicine 13 (1994), 1771-1780.
16. W. Y. Tsai and J. Crowley, A large sample study of the generalized maximum likelihood estimators from incomplete data via self-consistency, Ann. Statist. 13 (1985), 1317-1334.
17. W. Y. Tsai, S. Leurgans, and J. Crowley, Nonparametric estimation of a bivariate survival function in the presence of censoring, Ann. Statist. 14 (1986), 1351-1365.
18. B. W. Turnbull, The empirical distribution function with arbitrary grouped, censored and truncated data, J. Roy. Statist. Soc. Ser. B 38 (1976), 290-295.
19. M. J. Van der Laan, Efficient estimation in the bivariate censoring model and repairing NPMLE, Ann. Statist. 24 (1996), 596-627.
20. Q. Q. Yu, A. Schick, L. L. Li, and G. Y. C. Wong, Asymptotic properties of the GMLE in the case 1 interval-censorship model with discrete inspection times, Canad. J. Statist., to appear.
21. Q. Q. Yu, A. Schick, L. L. Li, and G. Y. C. Wong, Asymptotic properties of the GMLE of a survival function with case 2 interval-censored data, Statist. Prob. Lett. 37 (1998), 223-228.