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Estimating the Distribution Function Using Parametric Methods in Informative Model of Random Censorship from Both Sides

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2022)

Abstract

This paper focuses on the investigation of two semi-parametric estimators for distribution functions in an informative model of random censorship from both sides. During the investigation of these estimators, we utilized the characterization properties of the informative model to gather insights. Additionally, we discussed the properties of these estimators using numerical modeling methods.

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References

  1. Araujo, A., Gine, E.: The Central Limit Theorem for Real and Banach Valued Random Variables. Willey, New York (1980)

    MATH  Google Scholar 

  2. Abdushukurov, A.A.: Estimation of probability density and intensity function of the Koziol-Green model of random cencoring. Sankhya: Indian J. Stat. Ser. A. 48, 150–168 (1987)

    Google Scholar 

  3. Abdushukurov, A.A.: Random cencorship model from both sides and independence test for it. Report of Acad. Sci. Rep. Uz. Issue 11, 8–9 (1994). (in Russian)

    Google Scholar 

  4. Abdushukurov, A.A.: Nonparametric estimation of the distribution function based on relative risk function. Commun. Statist. Th. Meth. 27(8), 1991–2012 (1998)

    Article  MATH  Google Scholar 

  5. Abdushukurov, A.A., Abdikalikov, F.A.: Semiparametric estimator of mean conditional residual life function under informative random censoring from both sides. Appl. Math. 6, 319–325 (2015)

    Article  Google Scholar 

  6. Abdikalikov, F.A., Abdushukurov, A.A.: Semiparametric estimation of conditional survival function in informative regression model of random censorship from both sides. Statisticheskie Metody Otsenivaniya i Proverki Gipotes. Perm. Russia. Perm State Univ. Press. Issue 23, 145–162 (2012). (In Russian)

    Google Scholar 

  7. Billingsley, P.: Convergence of Probability Measures. Willey, New York (1968)

    MATH  Google Scholar 

  8. Chen, P.E., Lin, G.D.: Maximum likehood estimation of survival function under the Koziol-Green proportional hazards model. Statist. Probab. Lett. 5, 75–80 (1987)

    Article  MathSciNet  Google Scholar 

  9. Csörgő, S., Horväth, L.: On the Koziol-Green model of random censorship. Biometrika 68, 391–401 (1981)

    MathSciNet  MATH  Google Scholar 

  10. Csörgő, S.: Estimating in proportional hazards model of random censorship. Statistics 19, 437–463 (1988)

    Article  MathSciNet  Google Scholar 

  11. Csörgő, S.: Testing for the prorortional hazard model of random censorship. In: Proceedings Fourth Prague Symposium Asymptotic Statistics. Carles University Press. Prague, pp. 41–53 (1989)

    Google Scholar 

  12. Csörgő, S., Mielniczuk, J.: Density estimation in the simple proportional hazards model. Statist. Probab. Lett. 6, 419–426 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  13. Csörgő, S., Faraway, J.J.: The paradoxical nature of the proportional hazards model of random censorship. Statistics 31, 67–78 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dvoretzky, A., Kiefer, J., Wolfowitz, J.: Asymptotic minimax character of the sample distribution function and of the multinomil estimator. Ann. Math. Statist. 27, 642–669 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ghorai, J.: The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model. Statist. Probab. Lett. 41, 303–313 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Koziol, J.A., Green, S.B.: A Cramer-von Mises statistic for randomly censored data. Biometrika 63(3), 465–476 (1976)

    MathSciNet  MATH  Google Scholar 

  17. Hollander, M., Pena, E.: Families of confidence bands for the survival function under the general right censorship model and the Koziol-Green model. Canadian J. Statist. 17(1), 59–74 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mansurov, D.R.: Sequential empirical processes in informative models of incomplete observations. In: Materials of International Conference “Teoriya funcsiy odnogo i mnogich compleksnych peremennich”, November 26–28. Nukus, pp. 165–168 (2020)

    Google Scholar 

  19. Massart, P.: The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann. Probab. 18(3), 1269–1283 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pawlitschko, J.: A comparison of survival function estimators in the Koziol-Green model. Statistics 32, 277–291 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. de Una-Álvares, J.: Kernel distribution function estimation under the Koziol-Green model. J. Stat. Plan. Infer. 87, 199–219 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Mansurov Dilshod Ravilovich .

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Akhmedovich, A.A., Ravilovich, M.D. (2023). Estimating the Distribution Function Using Parametric Methods in Informative Model of Random Censorship from Both Sides. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2022. Communications in Computer and Information Science, vol 1803. Springer, Cham. https://doi.org/10.1007/978-3-031-32990-6_19

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  • DOI: https://doi.org/10.1007/978-3-031-32990-6_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32989-0

  • Online ISBN: 978-3-031-32990-6

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