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A characterization of normality via convex likelihood ratios

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  • Jacobovic, Royi
  • Kella, Offer

Abstract

This work includes a new characterization of the multivariate normal distribution. In particular, it is shown that a positive density function f is Gaussian if and only if the f(x+y)/f(x) is convex in x for every y. This result has implications to recent research regarding inadmissibility of a test studied by Moran (1973).

Suggested Citation

  • Jacobovic, Royi & Kella, Offer, 2022. "A characterization of normality via convex likelihood ratios," Statistics & Probability Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000542
    DOI: 10.1016/j.spl.2022.109455
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    References listed on IDEAS

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    1. Novak, S.Y., 2007. "A new characterization of the normal law," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 95-98, January.
    2. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    3. Ejsmont, Wiktor, 2016. "A characterization of the normal distribution by the independence of a pair of random vectors," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 1-5.
    4. Henze, Norbert & Jiménez–Gamero, M. Dolores & Meintanis, Simos G., 2019. "Characterizations Of Multinormality And Corresponding Tests Of Fit, Including For Garch Models," Econometric Theory, Cambridge University Press, vol. 35(3), pages 510-546, June.
    5. Damian Jelito & Marcin Pitera, 2021. "New fat-tail normality test based on conditional second moments with applications to finance," Statistical Papers, Springer, vol. 62(5), pages 2083-2108, October.
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