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On the non-stochastic ordering of some quadratic forms

Author

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  • Marchand, Éric
  • Strawderman, William E.

Abstract

For Y=‖aZ+θ‖2, a>0, Z∼Np(θ,Ip), θ≠{0}, we show that the distribution of Y is not stochastically ordered in a>0. We provide extensions to spherically symmetric, elliptically symmetric, and skew-normal distributions, as well as to other quadratic forms.

Suggested Citation

  • Marchand, Éric & Strawderman, William E., 2020. "On the non-stochastic ordering of some quadratic forms," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220301024
    DOI: 10.1016/j.spl.2020.108799
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    References listed on IDEAS

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    1. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    2. T. Cacoullos & M. Koutras, 1984. "Quadratic forms in spherical random variables: Generalized noncentral x2 distribution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(3), pages 447-461, September.
    3. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    Full references (including those not matched with items on IDEAS)

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