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Moments of random vectors with skew t distribution and their quadratic forms

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  • Kim, Hyoung-Moon
  • Mallick, Bani K.

Abstract

Moments of skew t random vectors and their quadratic forms are derived. It is shown that the moments of the sample autocovariance function and of the sample variogram estimator depend on a measure of multivariate kurtosis, but not on a skewness parameter.

Suggested Citation

  • Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:4:p:417-423
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    References listed on IDEAS

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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. 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.
    3. Gorsich, David J. & Genton, Marc G. & Strang, Gilbert, 2002. "Eigenstructures of Spatial Design Matrices," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 138-165, January.
    4. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    5. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    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.
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    Citations

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    Cited by:

    1. Umbach, Dale, 2008. "Some moment relationships for multivariate skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1619-1623, September.
    2. Jorge M. Arevalillo & Hilario Navarro, 2021. "Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    3. Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.
    4. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
    5. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    6. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2013. "The centred parameterization and related quantities of the skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 73-90.
    7. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    8. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    9. Nicola Loperfido, 2019. "Finite mixtures, projection pursuit and tensor rank: a triangulation," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 145-173, March.
    10. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    11. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.

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