Ghorai, J. K.; Rejtö, L. Estimation of mean residual life with censored data under the proportional hazard model. (English) Zbl 0646.62029 Commun. Stat., Theory Methods 16, 2097-2114 (1987). Large sample properties of an estimator of a truncated version of the mean residual life function are derived under the proportional hazard rate model. The estimator is based on the maximum likelihood estimator of the survival function. The properties established are uniform strong and mean square consistency as well as weak convergence to a Gaussian process. An asymptotic confidence interval for the truncated version of the mean residual life function is also obtained. Reviewer: S.N.U.A.Kirmani Cited in 9 Documents MSC: 62G05 Nonparametric estimation 62N05 Reliability and life testing 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics 62P10 Applications of statistics to biology and medical sciences; meta analysis Keywords:censored data; truncation; uniform strong consistency; Large sample properties; mean residual life function; proportional hazard rate model; maximum likelihood estimator of the survival function; mean square consistency; weak convergence to a Gaussian process; asymptotic confidence interval PDFBibTeX XMLCite \textit{J. K. Ghorai} and \textit{L. Rejtö}, Commun. Stat., Theory Methods 16, 2097--2114 (1987; Zbl 0646.62029) Full Text: DOI References: [1] Abdushukurov, A.A. On some estimates of the distribution function under random censorship. Conference of Young Scientists. Math. Inst. Acad. Sci. Tashkent: Uzbek SSR. VINITI No. 8756-V (in Russian) · Zbl 0653.62032 [2] Billingsley P., Convergence of Probability Measures (1968) · Zbl 0172.21201 [3] DOI: 10.1214/aos/1176342705 · Zbl 0283.62023 · doi:10.1214/aos/1176342705 [4] Cheng P.E., Maximum likelihood estimation of survival function under the Koziol-Green proportional hazard model (1984) [5] DOI: 10.2307/2335584 · doi:10.2307/2335584 [6] Ghorai J.K., Nonparametric Statistical Inference 32 pp 269– (1982) [7] Hall W.J., Estimation of mean residual life (1979) [8] DOI: 10.2307/2281868 · Zbl 0089.14801 · doi:10.2307/2281868 [9] Koziol J.A., Biometrika 63 pp 465– (1976) [10] DOI: 10.1007/BF01000216 · Zbl 0561.62032 · doi:10.1007/BF01000216 [11] DOI: 10.1007/BF00635964 · Zbl 0382.60031 · doi:10.1007/BF00635964 [12] DOI: 10.1214/aos/1176344070 · Zbl 0371.62055 · doi:10.1214/aos/1176344070 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.