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Nonparametric estimation of a distribution function from doubly truncated data under dependence

Author

Listed:
  • Carla Moreira

    (University of Minho)

  • Jacobo de Uña-Álvarez

    (SiDOR Research Group and CINBIO, University of Vigo)

  • Roel Braekers

    (Hasselt University)

Abstract

The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999). The consistency of the NPMLE depends however on the assumption of independent truncation. In this work we introduce an extension of the Efron–Petrosian NPMLE when the variable of interest and the truncation variables may be dependent. The proposed estimator is constructed on the basis of a copula function which represents the dependence structure between the variable of interest and the truncation variables. Two different iterative algorithms to compute the estimator in practice are introduced, and their performance is explored through an intensive Monte Carlo simulation study. We illustrate the use of the estimators on two real data examples.

Suggested Citation

  • Carla Moreira & Jacobo de Uña-Álvarez & Roel Braekers, 2021. "Nonparametric estimation of a distribution function from doubly truncated data under dependence," Computational Statistics, Springer, vol. 36(3), pages 1693-1720, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01085-4
    DOI: 10.1007/s00180-021-01085-4
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    References listed on IDEAS

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    1. Hong Zhu & Mei-Cheng Wang, 2014. "Nonparametric inference on bivariate survival data with interval sampling: association estimation and testing," Biometrika, Biometrika Trust, vol. 101(3), pages 519-533.
    2. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
    3. Austin, Matthew D. & Betensky, Rebecca A., 2014. "Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 16-26.
    4. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    5. T. Emura & K. Murotani, 2015. "An algorithm for estimating survival under a copula-based dependent truncation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 734-751, December.
    6. Lajmi Lakhal Chaieb & Louis-Paul Rivest & Belkacem Abdous, 2006. "Estimating survival under a dependent truncation," Biometrika, Biometrika Trust, vol. 93(3), pages 655-669, September.
    7. Emura, Takeshi & Wang, Weijing, 2012. "Nonparametric maximum likelihood estimation for dependent truncation data based on copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 171-188.
    8. Carla Moreira & Jacobo de Uña-Álvarez, 2010. "Bootstrapping the NPMLE for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 567-583.
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