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Fitting copulas in the case of missing data

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  • Eckhard Liebscher

    (University of Applied Sciences Merseburg)

Abstract

In this paper we deal with parametric estimation of the copula in the case of missing data. The data items with the same pattern of complete and missing data are combined into a subset. This approach corresponds to the MCAR model for missing data. We construct a specific Cramér–von Mises statistic as a sum of such statistics for the several missing data patterns. The minimization of the statistic gives the estimators for the parameters. We prove asymptotic normality of the parameter estimators and of the Cramér–von Mises statistic.

Suggested Citation

  • Eckhard Liebscher, 2024. "Fitting copulas in the case of missing data," Statistical Papers, Springer, vol. 65(6), pages 3681-3711, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01535-3
    DOI: 10.1007/s00362-024-01535-3
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    References listed on IDEAS

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    3. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    4. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
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