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Generalized copula-graphic estimator

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  • Jacobo Uña-Álvarez
  • Noël Veraverbeke

Abstract

In this paper, a copula-graphic estimator is proposed for censored survival data. It is assumed that there is some dependent censoring acting on the variable of interest that may come from an existing competing risk. Furthermore, the full process is independently censored by some administrative censoring time. The dependent censoring is modeled through an Archimedean copula function, which is supposed to be known. An asymptotic representation of the estimator as a sum of independent and identically distributed random variables is obtained, and, consequently, a central limit theorem is established. We investigate the finite sample performance of the estimator through simulations. A real data illustration is included. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:2:p:343-360
    DOI: 10.1007/s11749-012-0314-2
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    References listed on IDEAS

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    1. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    2. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
    3. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    4. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
    5. Lajmi Lakhal & Louis-Paul Rivest & Belkacem Abdous, 2008. "Estimating Survival and Association in a Semicompeting Risks Model," Biometrics, The International Biometric Society, vol. 64(1), pages 180-188, March.
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    Cited by:

    1. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    2. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
    3. Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    4. Liu, Yi & Wang, Qihua, 2015. "Copula-graphic estimators for the marginal survival function with censoring indicators missing at random," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 101-110.
    5. Sujica, Aleksandar & Van Keilegom, Ingrid, 2013. "Estimation of location and scale functionals in nonparametric regression under copula dependent censoring," LIDAM Discussion Papers ISBA 2013024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.

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