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Robust estimators and tests for bivariate copulas based on likelihood depth

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  • Denecke, Liesa
  • Müller, Christine H.

Abstract

Estimators and tests based on likelihood depth for one-parametric copulas are given. For the Gaussian and Gumbel copulas, it is shown that the maximum depth estimators are biased. They can be corrected and the new estimators are robust against contamination. For testing, simplicial likelihood depth is considered. Because of the bias of the maximum depth estimator, simplicial likelihood depth is not a degenerated U-statistic so that easily asymptotic [alpha]-level tests can be derived for arbitrary hypotheses. Tests are in particular investigated for the one-sided alternatives. Simulation studies for the Gaussian and Gumbel copulas show that the power of the first test is rather good, but the latter one has to be improved, which is also done here. The new tests are robust against contamination.

Suggested Citation

  • Denecke, Liesa & Müller, Christine H., 2011. "Robust estimators and tests for bivariate copulas based on likelihood depth," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2724-2738, September.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2724-2738
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    References listed on IDEAS

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    1. Lawless, Jerald F. & Yilmaz, Yildiz E., 2011. "Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2446-2455, July.
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    4. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, December.
    5. Ivan Mizera & Christine H. Muller, 2004. "Location-Scale Depth," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 949-966, December.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    7. Müller, Christine H., 2005. "Depth estimators and tests based on the likelihood principle with application to regression," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 153-181, July.
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    Cited by:

    1. Christoph P. Kustosz & Anne Leucht & Christine H. MÜller, 2016. "Tests Based on Simplicial Depth for AR(1) Models With Explosion," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 763-784, November.
    2. Davy Paindaveine & Germain Van Bever, 2017. "Halfspace Depths for Scatter, Concentration and Shape Matrices," Working Papers ECARES ECARES 2017-19, ULB -- Universite Libre de Bruxelles.
    3. Yihai He & Linbo Wang & Zhenzhen He & Xun Xiao, 2016. "Modelling infant failure rate of electromechanical products with multilayered quality variations from manufacturing process," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6594-6612, November.
    4. Liesa Denecke & Christine Müller, 2014. "Consistency of the likelihood depth estimator for the correlation coefficient," Statistical Papers, Springer, vol. 55(1), pages 3-13, February.
    5. Kotík, Lukáš & Hlubinka, Daniel, 2017. "A weighted localization of halfspace depth and its properties," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 53-69.
    6. Liesa Denecke & Christine Müller, 2014. "New robust tests for the parameters of the Weibull distribution for complete and censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 585-607, July.

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