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Minimum density power divergence estimator for covariance matrix based on skew $$t$$ t distribution

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  • Byungsoo Kim
  • Sangyeol Lee

Abstract

In this paper, we study the problem of estimating the covariance matrix of stationary multivariate time series based on the minimum density power divergence method that uses a multivariate skew $$t$$ t distribution family. It is shown that under regularity conditions, the proposed estimator is strongly consistent and asymptotically normal. A simulation study is provided for illustration. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Byungsoo Kim & Sangyeol Lee, 2014. "Minimum density power divergence estimator for covariance matrix based on skew $$t$$ t distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 565-575, November.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:565-575
    DOI: 10.1007/s10260-014-0284-5
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    References listed on IDEAS

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    1. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    2. Kim, Byungsoo & Lee, Sangyeol, 2013. "Robust estimation for the covariance matrix of multivariate time series based on normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 125-140.
    3. Byungsoo Kim & Sangyeol Lee, 2011. "Robust estimation for the covariance matrix of multi‐variate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 469-481, September.
    4. N. A. Campbell, 1980. "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 231-237, November.
    5. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    7. Álvarez Alvarado, Marcos Tulio, 2003. "¿Existe una alternativa al capitalismo?," Observatorio de la Economía Latinoamericana, Servicios Académicos Intercontinentales SL. Hasta 31/12/2022, issue 16, November.
    8. Seokho Lee & Marc G. Genton & Reinaldo B. Arellano-Valle, 2010. "Perturbation of Numerical Confidential Data via Skew-t Distributions," Management Science, INFORMS, vol. 56(2), pages 318-333, February.
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