Geodesic
On estimation of bivariate survival function from random censored data
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 422-430.

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At present there are several approaches to estimate survival functions of vectors of lifetimes. However, some of these estimators are either inconsistent or not fully defined in the range of joint survival functions. Therefore they are not applicable in practice. In this paper three types of estimates of exponential-hazard, product-limit and relative-risk power structures for the bivariate survival function are considered when the number of summands in empirical estimates is replaced with a sequence of Poisson random variables. It is shown that proposed estimates are asymptotically equivalent.
Keywords: bivariate survival function, empirical estimates.
Mots-clés : Poisson random variables 
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Abdurakhim A. Abdushukurov; Rustamjon S. Muradov. On estimation of bivariate survival function from random censored data. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 422-430. http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a3/

[1] A.A. Abdushukurov, “Nonparametrical estimators of survival function on the plane by censored observations”, Uzbek mathematical journal, 2 (2004), 3–11 (in Russian)

[2] A.A. Abdushukurov, Estimates of unknown distributions from incomplete observations and their properties, LAMBERT Academic Publishing, 2011 (in Russian)

[3] A.A. Abdushukurov, R.S. Muradov, “Estimation of two-dimensional survival function by random right censored Data”, Proc. of XI-th Intern. Conf. Computer Data Analysis and Modelling (Minsk, Belorus, 2016), 85–86

[4] A.A. Abdushukurov, “Estimation of joint survival function from censored observations”, Industrial Lab. Diagn. Mater., 82 (2016), 80–84 (in Russian)

[5] A.A. Abdushukurov, R.S. Muradov, “On the estimates of the distribution function in a random censorship model”, Industrial Lab. Diagn. Mater., 80 (2014), 62–67 (in Russian)

[6] A.A. Abdushukurov, R.S. Muradov, “On Estimation of Conditional Distribution Function under Dependent Random Right Censored Data”, Journal of Siberian Federal University, 7 (2014), 409–416

[7] A.A. Abdushukurov, R.S. Muradov, “Estimation of survival functions from dependent random right censored data”, Intern. J. Innovation in Science and Mathematics, 2 (2014), 280–287

[8] A.A. Abdushukurov, R.S. Muradov, “Some algebraic properties of Archimedean copula functions and their applications in the statistical estimation of the survival function”, New Trends in Math. Sci., 4 (2016), 88–98 | DOI

[9] M.D. Burke, “Estimation of a bivariate distribution function under random censorship”, Biometrika, 75 (1988), 379–382

[10] G. Campbell, “Nonparametric bivariate estimation with randomly censored data”, Biometrika, 68 (1981), 417–422

[11] G. Campbell, A. Földes, “Lange sample properties of nonparametric bivariate estimators with censored data”, Colloquia Mathematica-Societatis János Bolyai, 32, 1982, 103–122

[12] D.M. Dabrowska, “Kaplan-Meier estimate on the plane”, Ann. Statist., 16 (1988), 1475–1489

[13] D.M. Dabrowska, “Kaplan-Meier estimate on the plane: weak convergence, LIL and the bootstrap”, J. Multivar. Anal., 29 (1989), 308–325

[14] R.D. Gill, “Multivariate Survival Analysis I”, Theory Probab. Appl., 37 (1992), 19–35 (in Russian)

[15] R.D. Gill, “Multivariate Survival Analysis II”, Theory Probab. Appl., 37 (1992), 307–328 (in Russian)

[16] J.A. Hanley, M.N. Parnes, “Nonparametric estimation of a multivariate distribution in the presence of censoring”, Biometrica, 39 (1983), 129–139

[17] L. Horváth, “The rate of strong uniform consistency for the multivariate product-limit estimator”, J. Multivar. Anal., 13 (1983), 202–209

[18] Y. Huang, “Two-sample multistate accelerated sojourn times model”, J.A.S.A., 95 (2000), 619–627

[19] R.S. Muradov, A.A. Abdushukurov, Estimation of multivariate distributions and there mixes by incomplete data, LAMBERT Academic Publishing, Germany, 2011 (in Russian)

[20] W.Y. Tsai, S. Leurgans, J. Crowley, “Nonparametric estimation of a bivariate survival function in the presence of censoring”, Ann. Statist., 14 (1986), 1351–1365

[21] J.D. Fermanian, “Multivariate hazard rates under random censorship”, J. Multivar. Anal., 62 (1997), 273–309

[22] V.V. Petrov, Limit Theorems of Probability Theory: Sequence of independent r.v.-s., Oxford Studies in Probability-4, 4, Clerandon Press, Oxford, 1995