JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Estimation of Bivariate Survival Function for Possibly Censored Data
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Estimation of Bivariate Survival Function for Possibly Censored Data
Park Hyo-Il; Na Jong-Hwa;
  PDF(new window)
 Abstract
We consider to obtain an estimate of bivariate survival function for the right censored data with the assumption that the two components of censoring vector are independent. The estimate is derived from an ad hoc approach based on the representation of survival function. Then the resulting estimate can be considered as an extension of the Susarla- Van Ryzin estimate to the bivariate data. Also we show the consistency and weak convergence for the proposed estimate. Finally we compare our estimate with Dabrowska's estimate with an example and discuss some properties of our estimate with brief comment on the extension to the multivariate case.
 Keywords
bivariate survival function;consistency;Susarla- Van Ryzin estimate;weak convergence;
 Language
English
 Cited by
 References
1.
Andersen, P. K., Borgan, O, Gill, R. D. and Keiding, N. (1991). Statistical Models Based on Counting Processes, Springer, New York

2.
Burke, M. D. (1988). Estimation of a bivariate distribution function under random censorship, Biometrika, Vol. 75, 379-382 crossref(new window)

3.
Campbell, G. (1981). Nonparametric bivariate estimation with randomly censored data, Biometrika, Vol. 68, 417-422 crossref(new window)

4.
Campbell, G. (1982). Asymptotic properties of several nonparametric multivariate distribution function estimators under random censoring, In Survival Analysist(J. J. Crowley and R. A. Johnson, Eds.). IMS Lecture Notes Vol. 2, pp.243-256. Institute of Mathematical Statistics, Hayward, California

5.
Dabrowska, D. (1988). Kaplan-Meier estimate on the plane, Annals of Statistics, Vol. 16, 1475-1489 crossref(new window)

6.
Hanley, J. A. and Parnes, M. N. (1983). Nonparametric estimation of a multivariate distribution in the presence of censoring, Biometrics, Vol. 39, 129-139 crossref(new window)

7.
Hougaard, P. (2000). Analysis of Multivariate Survival Data, Springer, New York

8.
Korwar, R. and Dahiya, R. (1981). Estimation of a bivariate distribution function from incomplete observations, Communications in Statistics, Theory and Methods, Vol. 11, 887-897

9.
Prentice, R. L. and Cai, J. (1992). Covariance and survivor function estimation using censored multivariate time data, Biometrika, Vol. 79, 495-512 crossref(new window)

10.
Pruitt, R. C. (1991). On the negative mass assigned by the bivariate Kaplan-Meier estimator, Annals of Statistics, Vol. 19, 443-453 crossref(new window)

11.
Shorack, G. R. and Wellner, J. A. (1986). Empirical processes with applications to Statistics, Wiley and Sons, Inc. New York

12.
Susarla, V. and Van Ryzin, J. (1976). Nonparametric estimation of survival curves from incomplete observation, Journal of American Statistical Association, Vol. 71, 897-902 crossref(new window)

13.
Susarla, V. and Van Ryzin, J. (1978). Large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples, Annals of Statistics, Vol. 6, 755-768 crossref(new window)

14.
Susarla, V. and Van Ryzin, J. (1980). Large sample theory for an estimator of the mean survival time from censored samples, Annals of Statistics, Vol. 8, 1002-1016 crossref(new window)

15.
Tsai, W. Y. and Crowley, J, (1998). A note on nonparametric estimators of the bivariate survival function under univariate censoring, Biometrika, Vol. 85, 573-580 crossref(new window)

16.
Tsai, W. Y, Leurgans, S. and Crowley, J. (1986). Nonparametric estimation of a bivariate survival function in the presence of censoring, Annals of Statistics, Vol. 14, 1351-1365 crossref(new window)

17.
VanDer Laan, M. J. (1996). Efficient estimation in the bivariate censoring model and repairing NPMLE, Annals of Statistics, Vol. 24, 596-627 crossref(new window)