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Non-parametric Copula Estimation Under Bivariate Censoring

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  • Svetlana Gribkova
  • Olivier Lopez

Abstract

type="main" xml:id="sjos12144-abs-0001"> In this paper, we consider non-parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l-super-∞([0,1]-super-2). We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non-parametric estimators to define a goodness-of-fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:925-946
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    File URL: http://hdl.handle.net/10.1111/sjos.12144
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    References listed on IDEAS

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    Cited by:

    1. Franc{c}ois Dufresne & Enkelejd Hashorva & Gildas Ratovomirija & Youssouf Toukourou, 2016. "On bivariate lifetime modelling in life insurance applications," Papers 1601.04351, arXiv.org.
    2. Souto Arias, Luis A. & Cirillo, Pasquale, 2021. "Joint and survivor annuity valuation with a bivariate reinforced urn process," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 174-189.
    3. Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    4. Michaelides, Marie & Cossette, Hélène & Pigeon, Mathieu, 2026. "Parametric estimation of conditional archimedean copula generators for censored data," Computational Statistics & Data Analysis, Elsevier, vol. 216(C).

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