Estimation of Distribution Function Based on Presmoothed Relative-Risk Function
Abstract: In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.
Cite this paper: Abdushukurov, A. , Bozorov, S. and Mansurov, D. (2022) Estimation of Distribution Function Based on Presmoothed Relative-Risk Function. Applied Mathematics, 13, 191-204. doi: 10.4236/am.2022.132015.
References

[1]   Kaplan, E.L. and Meier, P. (1958) Nonparametric Estimation from Incomplete Observation. Journal of the American Statistical Association, 53, 457-481.
https://doi.org/10.1080/01621459.1958.10501452

[2]   Abdushukurov, A.A. (1998) Nonparametric Estimation of the Distribution Function Based on Relative-Risk Function. Communications in Statistics: Theory and Methods, 27, 1991-2012.
https://doi.org/10.1080/03610929808832205

[3]   Abdushukurov, A.A. (1999) On Nonparametric Estimation of Reliability Indices by Censored Samples. Theory of Probability & Its Applications, 43, 3-11.
https://doi.org/10.1137/S0040585X97976702

[4]   Abdushukurov, A.A. (2011) Estimation of Unknown Distributions from Incomplete Observations and their Properties. LAP Lambert Academic, Saarbrtücken. (in Russian)

[5]   Abdushukurov, A.A. (1987) Nonparametric Estimation in Proportional Hazards Model of Random Censorship. VINITI 3448 (B87).

[6]   Cheng, P.E. and Lin, G.D. (1987) Maximum Likelihood Estimation of Survival Function under the Koziol-Green Proportional Hazards Model. Statistics & Probability Letters, 5, 75-80.
https://doi.org/10.1016/0167-7152(87)90030-7

[7]   Csörgő, S. (1988) Estimation in the Proportional Hazards Model of Random Censorship. Statistics, 19, 437-463.
https://doi.org/10.1080/02331888808802115

[8]   Nadaraya, E.A. (1964) On Estimating Regression. Probability Theory and Related Fields, 61, 405-415.

[9]   Watson, G.S. (1964) Smooth Regression Analysis. Sankhya: The Indian Journal of Statistics, Series A, 26, 359-372.

[10]   Dikta, J. (1998) On Semiparametric Random Censorship Models. Journal of Statistical Planning and Inference, 66, 253-279.
https://doi.org/10.1016/S0378-3758(97)00091-8

[11]   Cao, R., Lopez-de-Ullibarri, I., Janssen, P. and Veraverbeke, N. (2005) Presmoothed Kaplan-Meier and Nelson-Aalen Estimators. Journal of Nonparametric Statistics, 17, 31-56.
https://doi.org/10.1080/10485250410001713981

[12]   Jacome, M.A. and Cao, R. (2007) Almost Sure Asymptotic Representation for the Presmoothed Distribution and Density Estimators for Censored Data. Statistics, 41, 517-534.
https://doi.org/10.1080/02331880701529522

[13]   Massart, P. (1990) The Tight Constant in the Dworetzky-Kiefer-Wolfowitz Inequality. Annals of Probability, 18, 1269-1283.
https://doi.org/10.1214/aop/1176990746

[14]   Burke, M.D., Csörgő, S. and Horvath, L. (1988) A Correction to and Improvement of “Strong Approximations of Some Biometric Estimates under Random Censorship”. Probability Theory and Related Fields, 79, 51-57.
https://doi.org/10.1007/BF00319103

Top