×

Strong approximations of some biometric estimates under random censorship. (English) Zbl 0439.60012


MSC:

60E05 Probability distributions: general theory
60G15 Gaussian processes
60F99 Limit theorems in probability theory
92B05 General biology and biomathematics
Full Text: DOI

References:

[1] Anderson, T. W., A modification of the sequential probability ratio test to reduce the sample size, Ann. Math. Statist., 31, 165-197 (1960) · Zbl 0089.35501
[2] Berman, S. M., A note on extreme values, competing risks and semi-Markov processes, Ann. Math. Statist., 34, 1104-1106 (1963) · Zbl 0203.21702
[3] Breslow, N.; Crowley, J., A large sample study of the life table and product limit estimates under random censorship, Ann. Statist., 2, 437-453 (1974) · Zbl 0283.62023
[4] Csörgő, M.; Révész, P., Strong approximations in probability and statistics (1981), New York: Academic Press, New York · Zbl 0539.60029
[5] Csörgő, S.: Limit behaviour of the empirical characteristic function. Ann. Probability 9, (1981) · Zbl 0453.60025
[6] Csörgő, S., Horváth, L.: On the Koziol-Green model of random censorship. Biometrika 68 (1981). To appear · Zbl 0493.62045
[7] Dvoretzky, A.; Kiefer, J.; Wolfowitz, J., Asymptotic minimax character of the sample distribution function and of the multinomial estimator, Ann. Math. Statist., 27, 642-669 (1956) · Zbl 0073.14603
[8] Efron, B., The two-sample problem with censored data, Proc. Fifth Berkeley Symp. Math. Statist. Probability, 4, 831-853 (1967)
[9] Földes, A., Rejtő, L.: Strong uniform consistency for non-parametric survival estimators from randomly censored data. Preprint · Zbl 0453.62034
[10] Földes, A., Rejtő, L.: Asymptotic properties of the non-parametric survival curve estimators under variable censoring. Preprint · Zbl 0468.62038
[11] Földes, A., Rejtő, L.: A LIL type result for the product limit estimator on the whole line. Preprint · Zbl 0443.62031
[12] Földes, A.; Rejtő, L.; Winter, B. B., Strong consistency properties of nonparametric estimators for randomly censored data, Trans. Eighth Prague Conference Information Theory etc. Vol. C, 105-121 (1979), Prague: Academia, Prague · Zbl 0414.62075
[13] Földes, A.; Rejtő, L.; Winter, B. B., Strong consistency properties of nonparametric estimators for randomly censored data, Periodica Math. Hung., 11, 233-250 (1980) · Zbl 0432.60038
[14] Gillespie, M. J.; Fisher, L., Confidence bands for the Kaplan-Meier survival curve estimate, Ann. Statist., 7, 920-924 (1979) · Zbl 0423.62085
[15] Horváth, L.; Vincze, I., Two-problems under random censorship (1980), Budapest: North-Holland, Budapest
[16] Kaplan, E. L.; Meier, P., Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc., 53, 457-481 (1958) · Zbl 0089.14801
[17] Komlós, J.; Major, P.; Tusnády, G., An approximation of partial sums of independent r.v.’s and the sample d.f. I, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32, 111-132 (1975) · Zbl 0308.60029
[18] Koziol, J. A.; Green, S. B., A Cramér-von Mises statistic for randomly censored data, Biometrika, 63, 465-474 (1976) · Zbl 0344.62018
[19] Meier, P.; Gani, J., Estimation of a distribution function from incomplete observations, Perspectives in Probability and Statistics, 67-87 (1975), New York: Academic Press, New York · Zbl 0339.62021
[20] Tsiatis, A., A nonidentifiability aspect of the problem of competing risks, Proc. Nat. Acad. Sci. U.S.A., 72, 20-22 (1975) · Zbl 0299.62066
[21] Tusnády, G.: Investigations of statistical hypotheses (in Hungarian). Candidatus dissertation. Hungarian Academy of Sciences (1978)
[22] Winter, B. B.; Földes, A.; Rejtő, L., Glivenko-Cantelli theorems for the product limit estimate, Problems of Control and Information Theory, 7, 213-225 (1978) · Zbl 0499.60035
[23] Yang, G. L., Estimation of a biometric function, Ann. Statist., 6, 112-116 (1978) · Zbl 0371.62055
[24] Yang, G., Life expectancy under random censorship, Stochastic Processes Appl., 6, 33-39 (1977) · Zbl 0372.62075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.