Extension of Relative-Risk Power Estimator under Dependent Random Censored Data

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Abstract

In this paper, the considered problem consists in estimation of conditional survival function by right random censoring model in the presence of a covariate. We propose a new estimator of conditional survival function which is extension of relative-risk power estimator of independent censoring and study its large sample properties. We present result of asymptotic normality with the same limiting Gaussian process as for copula-graphic estimator.

About the authors

A. A. Abdushukurov

Lomonosov Moscow State University

Author for correspondence.
Email: a_abdushukurov@rambler.ru
Tashkent, Uzbekistan

References

  1. Абдушукуров А. А. Статистика неполных наблюдений. - Ташкент: Университет, 2009
  2. Abdushukurov A. A. Nonparametric estimation of distribution function based on relative risk function// Commun. Statist. Theory Methods - 1998. - 27, № 8. - C. 1991-2012
  3. Abdushukurov A. A. On nonparametric estimation of reliability indices by censored samples// Theory Probab. Appl. - 1999. - 43, № 1. - C. 3-11
  4. Abdushukurov A. A., R. Muradov S. Estimation of survival and mean residual life functions from dependent random censored data// New Trends Math. Sci. - 2014. - 2, № 1. - C. 35-48
  5. Abdushukurov A. A., Muradov R. S. On estimation of conditional distribution function under dependent random right censored data// Журн. СФУ. Сер. матем. и физ. - 2014. - 7, № 4. - C. 409-416
  6. Breakers R., Veraverbeke N. A copula-graphic estimator for the conditional survival function under dependent censoring// Canad. J. Statist. - 2005. - 33, № 3. - C. 429-447
  7. Csorgo S. Universal Gaussian approximations under random censorship// Ann. Statist. - 1996. - 24, № 6. - C. 2744-2778.
  8. Fleming T. R., Harrington D. P. Counting Processes and Survival Analysis. - New York: Wiley, 1991
  9. Kaplan E. L., Meier P. Nonparametric estimation from incomplete observations// J. Am. Statist. Assoc. - 1958. - 53. - C. 457-481
  10. Nelsen R. B. An Introduction to Copulas. - New York: Springer, 1999
  11. Rivest L. P., Wells M. T. A martingall approach to the copula-graphic estimator for the survival function under dependent censoring// J. Multivariate Anal. - 2001. - 79. - C. 138-155
  12. Zeng M., Klein J. P. Estimates of marginal survival for dependent competing risks based on an assumed copula// Biometrika - 1995. - 82. - C. 127-138

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