Nonparametric estimators of the bivariate survival function under random censoring

Statistica Neerlandica

Volumn 51, Issue 2, 1997, Pages 178-200

  Van Der Laan, M J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bivariate right censored data; Nonparametric maximum likelihood estimator; Product integral; Self consistency equation

Indexed keywords

EID: 0031498948     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9574.00049     Document Type: Article

References (22)

1. BAKKER, D. M. (1990), Two nonparametric estimators of the survival function of bivariate right censored observations, Report BS-R9035, Centre for mathematics and computer science, Amsterdam.
2. DABROWSKA, D. M. (1988), Kaplan Meier estimate on the plane, Annals of Statistics 16, 1475-1489.
3. DABROWSKA, D. M. (1989), Kaplan Meier estimate on the plane: weak convergence, LIL, and the Bootstrap, Journal of Multivariate Analysis 29, 308-325.
4. DEMPSTER, A. P., N. M. LAIRD and D. B. RUBIN (1977), Maximum likelihood from incomplete data via the EM-algorithm, Journal of the Royal Statistical Society Series B 39, 1-38.
5. EFRON, B. (1967), The two sample problem with censored data, Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 831-853, Berkeley, University of California Press.
6. GILL, R. D. (1989), Non- and Semi-parametric Maximum likelihood estimators and the von Mises method (Part 1), Scandinavian Journal of Statistics 16, 97-128.
7. GILL, R. D. (1992), Multivariate survival analysis, Theory of Probability and its Applications (English Translation) 37, 18-31 and 284-301.
8. GILL, R. D. and S. JOHANSEN (1990), A survey of product integration with a view towards application in survival analysis, Annals of Statistics 18, 1501-1555.
9. GILL, R. D., M. J. VAN DER LAAN and J. A. WELLNER (1995), Inefficient estimators, Annales de l'Institut Henri Poincaré Section B: Calcul des Probabilité et Statistique 31, 547-597.
10. HEITJAN, D. F. and D. B. RUBIN (1991), Ignorability and coarse data, Annals of Statistics 19, 2244-2253.
11. VAN DER LAAN, M. J. (1992), Efficient estimator of the bivariate survival function for right censored data, Technical Report No. 337, Department of Statistics, University of California, Berkeley.
12. VAN DER LAAN, M. J. (1993), Efficient and inefficient estimation in semiparametric models, Phothesis, Utrecht University, ISBN 90-393-0339-8.
13. VAN DER LAAN, M. J. (1994), Modified EM-equations-estimator of the bivariate survival function. Mathematical Methods of Statistics 3, 213-243.
14. VAN DER LAAN, M. J. (1995a), An identity for linear parameters in convex models, Preprint Nr. 765, Department of Mathematics, University of Utrecht, Revised for publication in Annals of Statistics.
15. VAN DER LAAN, M. J. (1995b), Efficient estimator of the bivariate survival function and repairing NPMLE, To appear in Annals of Statistics.
16. VAN DER LAAN, M. J. (1996), Efficient and inefficient estimation in semiparametric models, C.W.I.-tract, Centre of Mathematics and Computer Science, Amsterdam.
17. PRENTICE, R. L. and J. CAI (1992a), Covariance and survivor function estimation using censored multivariate failure time data, Biometrika 79, 495-512.
18. PRENTICE, R. L. and J. CAI (1992b), Marginal and conditional models for the analysis of multivariate failure time data, in: Klein, J. P. and P. K. Goel (eds.). Survival analysis State of the art, Kluwer, Dordrecht.
19. PRUITT, R. C. (1991), Strong consistency of self-consistent estimators: general theory and an application to bivariate survival analysis, Technical Report nr. 543, University of Minnesota.
20. PRUITT, R. C. (1993), Small sample comparisons of six bivariate survival curve estimators, Journal of Statistical Computation and Simulation 45, 147-167.
21. TSAI, W.-Y., S. LEURGANS and J. CROWLEY (1986), Nonparametric estimation of a bivariate survival function in the presence of censoring, Annals of Statistics 14, 1351-1365.
22. TURNBULL, B. W. (1976), The empirical distribution with arbitrarily grouped censored and truncated data, Journal of the Royal Statistical Society Series B 38, 290-295.