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Consistency of the likelihood depth estimator for the correlation coefficient

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  • Liesa Denecke
  • Christine Müller

Abstract

Denecke and Müller (CSDA 55:2724–2738, 2011 ) presented an estimator for the correlation coefficient based on likelihood depth for Gaussian copula and Denecke and Müller (J Stat Planning Inference 142: 2501–2517, 2012 ) proved a theorem about the consistency of general estimators based on data depth using uniform convergence of the depth measure. In this article, the uniform convergence of the depth measure for correlation is shown so that consistency of the correlation estimator based on depth can be concluded. The uniform convergence is shown with the help of the extension of the Glivenko-Cantelli Lemma by Vapnik- C̃ ervonenkis classes. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:3-13
    DOI: 10.1007/s00362-012-0490-x
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    References listed on IDEAS

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    1. 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.
    2. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    3. Romanazzi, Mario, 2009. "Data depth, random simplices and multivariate dispersion," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1473-1479, June.
    4. Karl Mosler, 2003. "Central Regions and Dependency," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 5-21, March.
    5. Lu Lin & Minghua Chen, 2006. "Robust estimating equation based on statistical depth," Statistical Papers, Springer, vol. 47(2), pages 263-278, March.
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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. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.
    3. 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.
    4. 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.

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