Abstract
In this paper, a class of functionals of Kaplan-Meier estimator is investigated. Counting process martingale methods are used to show the asymptotic normality, and we establish a mean square error inequality and a probability inequality of them without the assumption thatF, G are continuous, where,F, G are survival time distribution and censoring time distribution respectively.
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References
Gijbels I, Veraverbeke N. Almost sure asympototic representation for a class of functionals of the Kaplan-Meier estimator. Ann Statist, 1991, 19(3): 1457–1470
Kaplan E L, Meier P. Nonparametric estimation from imcomplete observations. J Amer Statist Assoc, 1958, 53: 457–481
Gill R D. Large sample behavior of the product limit estimator on the whole line. Ann Statist, 1983, 11; 49–58
Shorack G R, Wellner J A. Empirical processes with applications to statistics. New York: John Wiley & Sons, 1986, 293–332
Major P, Rejtö L. Strong embedding of the estimator of the distribution function under random censorship. Ann Statist, 1988, 16(3): 1113–1132
Zheng Z K. Limit theorems for the ratio of the Kaplan-Meier estimation or Altshuler estimation to the true survival function. Acata Mathematica Sinica, New Series, 1994, 10(4): 337–347
Wang Q H. Some large sample properties of an estimator of the hazard function from randomly censored data. Chinese Science Bulletin, 1995, 40(8): 632–635
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This project is supported by China Postdoctoral Science Foundation
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Qihua, W. Some large sample results for a class of functionals of Kaplan-Meier estimator. Acta Mathematica Sinica 14, 191–200 (1998). https://doi.org/10.1007/BF02560206
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DOI: https://doi.org/10.1007/BF02560206