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Robustness properties of dispersion estimators

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  • Genton, Marc G.
  • Ma, Yanyuan

Abstract

In this paper, we derive the influence function of dispersion estimators, based on a scale approach. The relation between the gross-error sensitivity of dispersion estimators and the one of the underlying scale estimator is described. We show that for the bivariate Gaussian distributions, the asymptotic variance of covariance estimators is minimal in the independent case, and is strictly increasing with the absolute value of the underlying covariance. The behavior of the asymptotic variance of correlation estimators seems to be the opposite, i.e. maximal for independent data, and strictly decreasing with the absolute value of the underlying correlation. In particular, dispersion estimators based on M-estimators of scale are studied closely. The one based on the median absolute deviation is the most B-robust in the class of symmetric estimators. Some other examples are analyzed, based on the maximum likelihood and the Welsch estimator of scale.

Suggested Citation

  • Genton, Marc G. & Ma, Yanyuan, 1999. "Robustness properties of dispersion estimators," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 343-350, October.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:4:p:343-350
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    References listed on IDEAS

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    1. Genton, Marc G., 1998. "Asymptotic variance of M-estimators for dependent Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 255-261, June.
    2. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
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    Cited by:

    1. Christophe Croux & Catherine Dehon, 2008. "Robustness versus Efficiency for Nonparametric Correlation Measures," Working Papers ECARES 2008_002, ULB -- Universite Libre de Bruxelles.
    2. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    3. Dürre, Alexander & Vogel, Daniel & Fried, Roland, 2015. "Spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 89-105.
    4. Park, Yeonjoo & Kim, Hyunsung & Lim, Yaeji, 2023. "Functional principal component analysis for partially observed elliptical process," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    5. Ma, Yanyuan & Genton, Marc G., 2001. "Highly Robust Estimation of Dispersion Matrices," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 11-36, July.

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