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Distribution of matrix quadratic forms under skew-normal settings

Author

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  • Ye, Rendao
  • Wang, Tonghui
  • Gupta, Arjun K.

Abstract

For a class of skew-normal matrix distributions, the density function, moment generating function and independence conditions are obtained. The noncentral skew Wishart distribution is defined, and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, our main results are applied to two examples.

Suggested Citation

  • Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    • Handle: RePEc:eee:jmvana:v:131:y:2014:i:c:p:229-239
    DOI: 10.1016/j.jmva.2014.07.001
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    References listed on IDEAS

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    Cited by:

    1. Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    2. Li, Baokun & Tian, Weizhong & Wang, Tonghui, 2018. "Remarks for the singular multivariate skew-normal distribution and its quadratic forms," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 105-112.
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    4. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
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    6. Phil D. Young & Joshua D. Patrick & John A. Ramey & Dean M. Young, 2020. "An Alternative Matrix Skew-Normal Random Matrix and Some Properties," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 28-49, February.

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