Summary
Sequential fixed-width confidence bands for a distribution function are derived in the case, when the data are censored from the right. The Breslow-Crowley invariance principle for the Kaplan Meier estimate is extended to the random sample size situation. Also some simulation results are reported, which illustrate the behavior of the stopping times.
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References
Breslow N, Crowley J (1974) A large sample study of the life table and product limit estimates under random censorship. Ann Statist 2:437–453
Chow YS, Robbins H (1965) On the asymptotic theory of fixed-width sequential confidence intervals for the mean. Ann Math Statist 36:457–462
Fernandez PJ (1970) A weak convergence theorem for random sums of independent random variables. Ann Math Statist 41:710–712
Gaenssler P, Stute W (1987) Seminar on empirical processes. Birkhäuser, Basel
Hall WJ, Wellner JA (1980) Confidence bands for a survival curve from censored data. Biometrika 67:133–143
Kalbfleisch JD, Prentice RL (1980) The statistical analysis of failure time data. Wiley, New York
Koziol JA, Byar DP (1975) Percentage points of the asymptotic distributions of one and two sample K-S statistics for truncated or censored data. Technometrics 17:507–510
Miller RG Jr (1981) Survival analysis. Wiley, New York
Nelson W (1982) Applied life data analysis. Wiley, New York
Pyke R (1968) The weak convergence of the empirical process with random sample size. Proc Camb Phil Soc 64:155–160
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Dikta, G., Kurtz, B. & Stute, W. Sequential fixed-width confidence bands for distribution functions under random censoring. Metrika 36, 167–176 (1989). https://doi.org/10.1007/BF02614090
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DOI: https://doi.org/10.1007/BF02614090