On analysis of survival function estimators with its identifiability with model of right random censorship | Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaja tehnika i informatika – Tomsk State University Journal of Control and Computer Science. 2025. № 71. DOI: 10.17223/19988605/71/6

On analysis of survival function estimators with its identifiability with model of right random censorship

It is considered random censorship from the right. In this model we investigate basically three types of estimators of exponential, product and power types. We illustrative study all these estimators including its presmothed modifications comparatively. We demonstrate confidence bands for considered estimators by using natural and artificial censored observation. It is showed that presmoothed power estimators have some peculiarities with respect to exponential and product-type estimators. It is shown that only power estimator has identifiability property with respect to right random censoring model in the case of a finite-size sample. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests

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Keywords

model of right random censorship, survival function, exponential, product and power estimators, presmoothed kernel estmators

Authors

Name	Organization	E-mail
Abdushukurov Abdurakhim A.	Moscow State University, Branch in Tashkent	a_abdushukurov@rambler.ru
Bozorov Sukhrob B.	Gulistan State University	suxrobbek_8912@mail.ru

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References

Abdushukurov, A.A., Bozorov, S.B., & Mansurov, D.R. (2024) Optimal kernel density estimation by statistical modeling with random censoring of observations. Vestnik Tomskogo gosudarstvennogo universiteta. Upravleniye, vychislitel'naya tekhnika i informatika - Tomsk State University Journal of Control and Computer Science. 67. pp. 49-59. DOI: 10.17223/19988605/67/6.

Akritas, M.G. (2000) The central limit theorem under censoring. Bernulli. 6(6). pp. 1109-1120.

Breslow, N. (1972). Discussion of professor Cox’s paper. Journal of Royal Statistics Society. 34(A). pp. 216-217.

Breslow, N. & Crowley, J. (1974) A large sample study of the life table and product-limit estimates under random censorship. Annual Statistics. 2. pp. 437-453.

Burke, M.D., Csorgo, S. & Horvath, L. (1981) Strong approximations some biometric estimates under random censorship. Z. Wahrscheinlich. Verw. Gebiete. 56. pp. 87-112.

Burke, M.D., Csorgo, S. & Horvath, L. (1988) A correction toand improvement of “Strong approximations of some biometric estimates under random censorship.” Probability Theory and Related Fields. 79. pp. 51-57.

Csorgo, S. (1996). Universial Gaussian approximations under random censorship. Annual Statistics. 24(6). pp. 2744-2778.

Csorgo, S., & Horvath, L. (1982). On random censorship from the right. Acta Sci. Math. 44. pp. 23-34.

Kaplan, E.L. & Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of American Statistics Association. 53. pp. 457-481.

Abdushukurov, A.A., & Mansurov, D.R. (2023) Estimating the distribution function using parametric methods in informative model of random censorship from both siodes. In: Dudin, A., Nazarov, A. & Moiseev, A. (eds) Communication in Computer and Information Sciences (CCIS). Springer. pp. 2025-2037.

Altshuler, B. (1970) Theory of measurements for competing risks in animal expriments. Math. Bioscieces. 6. pp. 1-11.

Abdushukurov, A.A. (1998) Nonparametric estimation of the distribution function based on relative risk function.Communication in Statististics - Theory & Methods. 27(8). pp. 1991-2012.

Abdushukurov, A.A. (1999) On nonparametric estimation of probability indices by censored samples. Theory of Probability and its Applications. 43(1). pp. 3-11.

Abdushukurov, A.A. (2011) Estimation of Unknown Distributions by Incomplete Observations. LAMBERT Academic Publishing (LAP).

Jacome, M.A. & Cao, R. (2004) Presmoothed kernel density estimator for censored data. Journal of Nonparam. Statist. 16. pp. 289-309.

Abdushukurov, A.A. (1987) Nonparametric estimation in Proportional Hazards Model. Technical Repert N3448-B -87.

Abdushukurov, A.A. (1987) Estimating of probability density and intensity functions of the Koziol-Green model of random censoring. Sankhya Indiren Journal of Statistics. 48(1). pp. 150-168.

Cheng, P.E. & Ling, G.D. (1987) Maximum likelihood estimation of a survival function under Koziol-Green proportional hazards model. Statist. Probability Letters. 5. pp. 75-80.

Csorgo, S. (1989) Testing for the proportional hazards model of random censorship. Proceedings IVPrague Symp. Asump. Statist. Charles Univ. Press. Prague. pp. 41-53.

Abdushukurov, A.A., Nurmukhamedova, N.S. & Bozorov, S.B. (2021) Nonparametric estimation of the distribution function under right random censoring based on presmoothed relative risk function. Lobachevskii Journal of Mathematics. 42(2). pp. 257-268.

Efron, B. (1981) Censored data and the Bootstrap. The Journal of the Acoustical Society of America. 76(374). pp. 312-319.

Csorgo, S. & Horvath, L. (1986) Confidence bands from censored samples. Canadian Journal of Statistics. 14(2). pp. 131-144.