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Nonparametric estimation for doubly censored failure time data. (English) Zbl 1172.62006
Summary: This paper considers the nonparametric estimation of a failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, the failure time of interest is defined as the elapsed time between an initial event and a subsequent event, and the observations on both events can suffer from censoring. As a consequence, the estimation is much more complicated than that for right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad hoc approaches as the asymptotic properties of the resulting estimates are basically unknown.
We investigate both the consistency and the convergence rate of a commonly used nonparametric estimate and show that as expected, the estimate is slower than that with right-censored or interval-censored data. Furthermore, we establish the asymptotic normality of the smooth functionals of the estimate and present a nonparametric test procedure for treatment comparison.

MSC:
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62G07 Density estimation
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[1] DOI: 10.2307/2532030 · Zbl 0715.62223 · doi:10.2307/2532030
[2] DOI: 10.1023/A:1012596731505 · Zbl 1116.62344 · doi:10.1023/A:1012596731505
[3] DOI: 10.1080/10485259608832677 · Zbl 0872.62039 · doi:10.1080/10485259608832677
[4] DOI: 10.2307/2533210 · Zbl 0826.62088 · doi:10.2307/2533210
[5] DOI: 10.1080/02664769922647 · Zbl 1072.62553 · doi:10.1080/02664769922647
[6] DOI: 10.2307/2533008 · Zbl 0875.62497 · doi:10.2307/2533008
[7] DOI: 10.1023/A:1009609227969 · Zbl 1089.62534 · doi:10.1023/A:1009609227969
[8] DOI: 10.1016/S0167-7152(01)00160-2 · Zbl 0994.62024 · doi:10.1016/S0167-7152(01)00160-2
[9] Groeneboom P., Lectures on inverse problems, in Lectures on Probability Theory and Statistics (Ecole d’Eté de Probabilités de Saint-Flour XXIV-1994) 1648 (1996)
[10] DOI: 10.1016/j.jmva.2005.07.006 · Zbl 1333.62129 · doi:10.1016/j.jmva.2005.07.006
[11] DOI: 10.1111/1467-9574.00050 · Zbl 0891.62033 · doi:10.1111/1467-9574.00050
[12] DOI: 10.1214/aos/1018031211 · Zbl 0954.62034 · doi:10.1214/aos/1018031211
[13] DOI: 10.1002/(SICI)1097-0258(19991130)18:22<3089::AID-SIM191>3.0.CO;2-0 · doi:10.1002/(SICI)1097-0258(19991130)18:22<3089::AID-SIM191>3.0.CO;2-0
[14] DOI: 10.1198/106186001317114901 · Zbl 04568630 · doi:10.1198/106186001317114901
[15] DOI: 10.2307/3316096 · Zbl 1018.62022 · doi:10.2307/3316096
[16] DOI: 10.1198/1061860043371 · doi:10.1198/1061860043371
[17] DOI: 10.1007/978-3-0348-8621-5 · doi:10.1007/978-3-0348-8621-5
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