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Estimation of bivariate and marginal distributions with censored data

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  • Michael G. Akritas
  • Ingrid Van Keilegom

Abstract

Summary. Consider a pair of random variables, both subject to random right censoring. New estimators for the bivariate and marginal distributions of these variables are proposed. The estimators of the marginal distributions are not the marginals of the corresponding estimator of the bivariate distribution. Both estimators require estimation of the conditional distribution when the conditioning variable is subject to censoring. Such a method of estimation is proposed. The weak convergence of the estimators proposed is obtained. A small simulation study suggests that the estimators of the marginal and bivariate distributions perform well relatively to respectively the Kaplan–Meier estimator for the marginal distribution and the estimators of Pruitt and van der Laan for the bivariate distribution. The use of the estimators in practice is illustrated by the analysis of a data set.

Suggested Citation

  • Michael G. Akritas & Ingrid Van Keilegom, 2003. "Estimation of bivariate and marginal distributions with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 457-471, May.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:457-471
    DOI: 10.1111/1467-9868.00396
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    Citations

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    Cited by:

    1. Alan D. Hutson, 2016. "Nonparametric rank based estimation of bivariate densities given censored data conditional on marginal probabilities," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-14, December.
    2. Gribkova, Svetlana & Lopez, Olivier & Saint-Pierre, Philippe, 2013. "A simplified model for studying bivariate mortality under right-censoring," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 181-192.
    3. Ross L. Prentice & Shanshan Zhao, 2018. "Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan–Meier estimator," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 3-27, January.
    4. Candida Geerdens & Gerda Claeskens & Paul Janssen, 2016. "Copula based flexible modeling of associations between clustered event times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 363-381, July.
    5. Emura, Takeshi & Kao, Fan-Hsuan & Michimae, Hirofumi, 2014. "An improved nonparametric estimator of sub-distribution function for bivariate competing risk models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 229-241.
    6. Dai, Hongsheng & Bao, Yanchun, 2009. "An inverse probability weighted estimator for the bivariate distribution function under right censoring," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1789-1797, August.
    7. Svetlana Gribkova & Olivier Lopez, 2015. "Non-parametric Copula Estimation Under Bivariate Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 925-946, December.
    8. Lopez, Olivier, 2012. "A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 505-516.

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