×
Abdushukurov, A. A.; Sagidullaev, K. S.

Asymptotic decompositions for numerical characteristics of the estimator of a mean residual life function. (English. Russian original) Zbl 06764448

J. Math. Sci., New York 221, No. 4, 487-495 (2017); translation from Statisticheskie Metody Otsenivaniya i Proverki Gipotez 20, 72-81 (2007).
Summary: This paper studies a nonparametric kernel estimator of a mean residual life function. We find asymptotic decompositions for the mean, variance, and mean square deviation of the estimator.

MSC:

62N05 Reliability and life testing
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

nonparametric kernel estimator; mean residual life function; asymptotic decompositions; mean; variance; mean square deviation
Cite Review PDF
Full Text: DOI

References:

[1] A. A. Abdushukurov and K. S. Sagidullaev, “Kernel estimation of a mean residual life function by the full time to failures,” in: Proceedings of the Universities, FAN, Tashkent (2003), pp. 41-50.
[2] A. A. Abdushukurov and K. S. Sagidullaev, “Bootstrap kernel estimation of mean residual life function,” J. Math. Sci., 189, No. 6, 884-888 (2013). · Zbl 1267.62051 · doi:10.1007/s10958-013-1227-7
[3] Sh. A. Khashimov and K. S. Sagidullaev, “On the asymptotic properties of a certain nonparametric estimator,” Uzbek. Math. J., 4, 73-78 (2000).
[4] A. Azzalini, “A note on the estimation of a distribution function and quantiles by a kernel method,” Biometrika, 68, 326-328 (1981). · Zbl 1267.62051
[5] Sh. A. Khashimov, “On the estimation of the hazard rate function,” in: Modern Problems of Probability Theory and Mathematical Statistics, FAN, Tashkent (2000), pp. 198-207.
[6] J. W. H. Swanepoel and F.C. Van Graan, “A new kernel distribution function estimator based on a non-parametric transformation of the data,” Scand. J. Stat., 32, 551-562 (2005). · Zbl 1091.62025 · doi:10.1111/j.1467-9469.2005.00472.x
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.