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A LIL type result for the product limit estimator. (English) Zbl 0443.62031

MSC:
62G05Nonparametric estimation
62N05Reliability and life testing (survival analysis)
60F15Strong limit theorems
References:
[1]Burke, M.D., Csörgo, S., Horváth, L.: Strong approximation of some biometric estimates under random censorship. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 87–112 (1981) · Zbl 0452.60021 · doi:10.1007/BF00531976
[2]Dvoretzky, A., Kiefer, I., Wolfowitz, I.: Asymptotic minmax character of the sample distribution function and the classical multinomial estimator. Ann. Math. Stat. 27, 642–669 (1956) · Zbl 0073.14603 · doi:10.1214/aoms/1177728174
[3]Földes, A., Rejto, L.: Strong uniform consistency for nonparametric survival estimators from randomly censored data. Annals of Statist. 9 (1981) (to appear)
[4]Földes, A., Rejto, L.: Asymptotic properties of the nonparametric survival curve estimators under variable censoring. Proc. of First Pannon Conf. in Statist. Springer-Verlag (To appear)
[5]Földes, A., Rejto, L., Winter, B.B.: Strong consistency properties of nonparametric estimators for randomly censored data. Periodica Math. Hung. 11, 233–250 (1980) · Zbl 0432.60038 · doi:10.1007/BF02026619
[6]Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observation. J. Amer. Statist. Assoc. 58, 457–481 (1963)
[7]Kiefer, I.: On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm. Pacific J. Math. 11, 649–660 (1961)
[8]Phadia, E.G., Van Ryzin, J.: A note on convergence rates for the P.L. estimator. [To appear)
[9]Susarla, V., van Ryzin, J.: Large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples. Ann. Statist. 6, 755–768 (1978) · Zbl 0378.62019 · doi:10.1214/aos/1176344250
[10]Wellner, Jon A.: Limit theorems for the ratios of the true distribution. Z. Wahrscheinlichkeitstheorie verw. Gebiete 45, 73–88 (1978) · Zbl 0382.60031 · doi:10.1007/BF00635964
[11]Komlós, J., Major, P., Tusnády, G.: An approximation of partial sums of independent random variables and the sample distribution function I. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32, 111–131 (1975) · Zbl 0308.60029 · doi:10.1007/BF00533093