Bivariate distribution and hazard functions when a component is randomly truncated

Journal of Multivariate Analysis

Volumn 60, Issue 1, 1997, Pages 20-47

  Gürler, Ülkü ^a  

^a BILKENT UNIVERSITY   (Turkey)

Author keywords

Bivariate distribution; Bivariate diverse hazard; Nonparametric estimation; Truncation; Weak convergence

Indexed keywords

EID: 0030672166     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.1630     Document Type: Article

References (23)

1. [1] Campbell, G. (1981). Nonparametric bivariate estimation with randomly censored data. Biometrika 68 417-442.
2. [2] Cox, D. R. (1972). Regression models and life-tables. J. Roy. Statist. Soc. Ser. B 34 187-220.
3. [3] Chao, M. T., and Lo, S. H. (1968). Some representations of the nonparametric maximum likelihood estimators with truncated data. Ann. Statist. 16 661-668.
4. [4] Dabrowska, D. M. (1988). Kaplan-Meier estimate on the plane. Ann. Statist. 16 1485-1489.
5. [5] Gijbels, I., and Wang, J. L. (1993). Strong representations of the survival function estimator for truncated and censored data with applications. J. Multivariate Anal. 47 210-229.
6. [6] Gross, S. T., and Huber-Carol, C. (1992). Regression models for truncated survival data. Scand. J. Statist. 19 193-213.
7. [7] Gu, M. G., and Lai, T. L. (1990). Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation. Ann. Probab. 18 160-189.
8. [8] Gürler, Ü. (1996). Bivariate estimation with right truncated data. J. Amer. Statist. Assoc. 91 1152-1165.
9. [9] Gürler, Ü. (1995). "Variance of the estimator for the bivariate distribution function when a component is truncated," IEOR-9515, Bilkent University, Dept. of Indust. Eng., 06533 Ankara, Turkey.
10. [10] Gürler, Ü., Stute, W., and Wang, J.-L. (1993). Weak and strong quantile representations for randomly truncated data with applications. Statist. Probab. Lett. 17 139-148.
11. [11] Kalbfleisch, J. D., and Lawless, J. F. (1989). Inference based on retrospective ascertainment: An analysis of the data on transfusion-related AIDS. J. Amer. Statist. Assoc. 84 360-372.
12. [12] Lai, T. L., and Ying, Z. (1991). Estimating a distribution function with truncated and censored data. Ann. Statist. 19 417-442.
13. [13] Leurgans, S. (1987). Linear models, random censoring and synthetic data. Biometrika 74 301-309.
14. [14] Lo, S. H., and Wang, J. L. (1989), I.I.D. representations for the bivariate product limit estimators and the bootstrap versio ns. J. Multivariate Anal. 28 211-226.
15. [15] Lynden-Bell, D. (1971). A method of allowing for known observational selection in small samples applied to 3CR quasars. Mon. Nat. Roy. Astr. Soc. 155 95-118.
16. [16] Neuhaus, G. (1971). On weak convergence of stochastic processes with multidimensional time parameter. Ann. Math. Statist. 42 1285-1295.
17. [17] Stute, W. (1993). Almost sure representations of the product-limit estimator for truncated data. Ann. Statist. 21 146-156.
18. [18] Stute, W. (1993). Consistent estimation under random censorship when covariables are present. J. Multivariate Anal. 45 89-103.
19. [19] Uzunoǧullari, Ü., and Wang, J.-L. (1992). A comparison of the hazard rate estimators for left truncated and right censored data. Biometrika 79 297-310.
20. [20] van der Laan, M. J. (1992), "Efficient estimator of the bivariate survival function for right censored data," Tech. rep., Department of Mathematics, University of Utrecht, The Netherlands.
21. [21] Wang, M. C., Jewell, N. P., and Tsai, W. Y. (1986). Asymptotic properties of the product limit estimate under random truncation. Ann. Statist. 14 1597-1605.
22. [21] Wang, M. C., Jewell, N. P., and Tsai, W. Y. (1986). Asymptotic properties of the product limit estimate under random truncation. Ann. Statist. 14 1597-1605.
23. [22] Woodroofe, M. (1985). Estimating a distribution function with truncated data. Ann. Statist. 13 163-177.