Density Estimation with Bivariate Censored Data

Journal of the American Statistical Association

Volumn 91, Issue 436, 1996, Pages 1566-1574

  Wells, Martin T ^a   Yeo, Kwee Poo ^b  

^a Department of Obstetrics Gynecology   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Bivariate failure time data; Kernel density estimation; Strong approximation; Survival analysis

Indexed keywords

EID: 0041856460     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476724     Document Type: Article

References (30)

1. Breslow, N. E., and Crowley, J. J. (1974), "A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship," TheAnnals of Statistics, 2, 437-453.
2. Campbell, G. (1981), "Nonparametric Bivariate Estimation With Censored Data," Biometrika, 68, 417-423.
3. Campbell, G., and Foldes, A (1982), "Large Sample Properties of Nonparametric Bivariate Estimators With Censored Data," in International Colloquium on Nonparametric Statistical Inference, Budapest 1980, Amsterdam: North-Holland, pp. 23-28.
4. Dabrawska, D. (1988), "Kaplan-Meier in the Plane," The Annals of Statistics, 16, 1475-1489.
5. Dabrawska, D (1989), "Kaplan-Meier on the Plane: Weak Convergence, LIL, and the Bootstrap," Journal of Multivariate Analysis, 29, 308-325.
6. Efron, B. (1967), "The Two-Samples Problem With Censored Data," Proceedings of the Fifth Berkeley Symposium, 4, 831--853.
7. Epanechnikov, V. A. (1969), "Nonparametric Estimation of a Multidimensional Probability Density," Theoretical Probability and Its Applications, 14, 153-158.
8. Foldes, A, Rejto, L., and Winter, B. B. (1980), "Streng Consistency Properties of Nonparametric Estimators for Randomly Censored Data, I: The Product-Limit Estimator," Periodica Mathematica Hungarica, 11, 233-250.
9. Foldes, A, Rejto, L., and Winter, B. B. (1981), "Strong Consistency Properties of Nonparametric Estimators for Randomly Censored Data, II: Estimation of Density and Failure Rate," Periodica Mathematica Hungarica, 12, 15-29.
10. Gill, R. D. (1983), "Large Sample Behavior of the Product-Limit Estimator on the Whole Line," The Annals of Statistics, 11,49-58.
11. Hall, P. (1983), "Large Sample Optimality of Least Squares CrossValidation in Density Estimation," The Annals of Statistics, 11, 1156-1174.
12. Hall, P. (1985), "Asymptotic Theory of Minimum In:egrated Square Error for Multivariate Density Estimation," in Multivariate Analysis VI, ed. P. R. Krishnaiah, Amsterdam: North-Holland, pp. 289-309.
13. Hall, P., and Wehrly, T. S. (1991), "A Geometrical Method for Removing Edge Effects From Kernel-Type Nonparametric Regression Estimators," Journal of the American Statistical Association, 85, 665-672.
14. Kaplan, E. L., and Meier, P. (1958), "Nonparametric Estimation From Incomplete Observations," Journal ofthe American Statistical Association, 53, 457-481. Journal of the American Statistical Association, December 1996
15. Lo, S. H., and Wang, J. L. (1989), "I.I.D. Representations for the Bivariate Product Limit Estimators and the Bootstrap Versions," Journal of Multivariate Analysis, 28, 211-226.
16. Marron, J. S., and Padgett, W. J. (1987), "Asymptotically Optimal Bandwidth Selection for Kernel Density Estimators From Randomly RightCensored Samples," The Annals of Statistics, 15, 1520-1535.
17. McNichols, D. T., and Padgett, W. J. (1986), "Mean and Variance of a Kernel Density Estimator Under Koziol-Green Model of Random Censorship," Sankhya, Ser, A, 48, 150-168.
18. Mielniczuk, I. (1986), "Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data," The Annals of Statistics, 14, 766-773.
19. Miller, R. G. (1981), Survival Analysis, New York: Wiley.
20. Miiller, H. G. (1984), "Boundary Effects in Nonparametric Curve Estimation Models," in Compstat 1984, eds. T. Havranek, A Sidak, and M. Novak, Vienna: Physica-Verlag, pp. 84-89.
21. Miiller, H. G., and Wang, J. L. (1990), "Locally Adaptive Hazard Smoothing," Probability Theory and Related Fields, 85, 523-538.
22. Prentice, R. L., and Cai, J. (1992), "A Covariance Function for Bivariate Survival Data and a Bivariate Survivor Function Estimate," Biometrika, 79, 495-512.
23. Pruit, R. (1991), "On Negative Mass Assigned by the Bivariate KaplanMeier," The Annals of Statistics, 19,443-453.
24. Pruit, R (1993), "Small Sample Comparisons of Six Bivariate Survival Curve Estimators," Journal of Statistical Computation and Simulation, 45, 147-167.
25. Rice, J. (1984), "Boundary Modification for Kernel Regression," Communications in Statistics, Part A-Theory and Methods, 13, 893-900.
26. Schuster, E. F. (1985), "Incorporating Support Constraints Into Nonparametric Estimation of Densities," Communications in Statistics, PartATheory and Methods, 14, 1123-1136.
27. Tsai, W. Y, Leurgans, S., and Crowley, J. (1986), "Nonparametric Estimation of a Bivariate Survival Function in the Presence of Censoring," The Annals of Statistics, 14, 1351-1365.
28. van der Laan, M. J. (1993), "Efficient and Inefficient Estimation in Semiparametric Models," Ph.D. thesis, University of Utrecht.
29. Yeo, K. P., and Wells, M. T. (1993), "Density Estimation with Censored Data," technical report, Cornell University Statistics Center.
30. Yeo, K. P., and Wells, M. T. (1994), "Bandwidth Selection for Density Estimators with Bivariate Censored Data," technical report, Cornell University Statistics Center.