In the paper, the empirical process in informative model of random censorship from both sides is investigated. For it, the limit Gaussian process with mean zero is founded. Under investigating of empirical process, the characterization properties of the considered informative model is used. The properties of the semiparametric estimator by using methods of numerical modeling are discussed.
1. Araujo A., Gine E. The central limit theorem for real and Banach valued random variables. Willey. New York (1980).
2. Abdushukurov A.A. Estimation of probability density and intensity function of the Koziol-Green model of random cencoring. Sankhya: Indian J. Statistics, Ser.A. Vol. 48, 150-168 (1987).
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).
4. Abdushukurov A.A. Nonparametric estimation of the distribution function based on relative risk function. Commun. Statist: Th. & Meth. Vol. 27, No. 8, 1991-2012 (1998).
5. Abdushukurov A.A., Abdikalikov F.A. Semiparametric estimator of mean conditional residual life function under informative random cencoring from both sides. Applied Mathematics. Vol. 6, 319-325 (2015).
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).
7. Billingsley P. Convergence of probability measures. Willey. New York (1968).
8. Chen P.E., Lin G.D. Maximum likehood estimation of survival function under the Koziol-Green proportional hazards model. Statist. Probab. Letters. Vol. 5, 75-80 (1987).
9. Csörgő S., Horväth L. On the Koziol-Green model of random censorship. Biometrika. Vol. 68, 391-401 (1981).
10. Csörgő S. Estimating in proportional hazards model of random censorship. Statistics. Vol. 19, 437-463 (1988).
11. Csörgő S. Testing for the prorortional hazard model of random censorship. Proc. fourth Prague Symp. Asymp. Statist. Carles Univ. Press. Prague, 41-53 (1989).
12. Csörgő S., Mielniczuk J. Density estimation in the simple proportional hazards model. Statist. Probab. Letters. Vol. 6, 419-426 (1988).
13. Csörgő S., Faraway J.J. The paradoxical nature of the proportional hazards model of random censorship. Statistics. Vol. 31, 67-78 (1998).
14. Dvoretzky A., Kiefer J., Wolfowitz J. Asymptotic minimax character of the sample distribution function and of the multinomil estimator. Ann. Math. Statist. Vol. 27, 642-669 (1956).
15. Ghorai J. The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model. Statist. Probab. Letters. Vol. 41, 303-313 (1999).
16. Koziol J.A., Green S.B. A Cramer-von Mises statistic for randomly censored data. Biometrika. Vol. 63, No. 3, 465-476 (1976).
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. Vol. 17, No. 1, 59-74 (1989).
18. Mansurov D.R. Sequential empirical processes in informative models of incomplete observations. Materials of international conf. "Teoriya funcsiy odnogo i mnogich compleksnych peremennich" November 26-28. Nukus, 165-168 (2020).
19. Massart P. The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann. Probab. Vol. 18, No. 3, 1269-1283 (1990).
20. Pawlitschko J. A Comparison of survival function estimators in the Koziol-Green model. Statistics. Vol. 32, 277-291 (1999).
21. De Una-Álvares J. Kernel distribution function estimation under the Koziol-Green model. J. Stat. Plan. Infer. Vol. 87, 199-219 (2000).
Abdushukurov, Abdurakhim and Mansurov, Dilshod
"Asymptotic results for empirical processes in informative model of random censorship from both sides,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 4:
3, Article 2.