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Linear transformations to symmetry

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  • Loperfido, Nicola

Abstract

We obtain random vectors with null third-order cumulants by projecting the data onto appropriate subspaces. Statistical applications include, but are not limited to, the robustification of Hotelling’s T2 test against nonnormality. Our approach only requires the existence of the third-order moments and leads to normal transformed variables when the parent distribution belongs to well-known classes of sample selection models.

Suggested Citation

  • Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:186-192
    DOI: 10.1016/j.jmva.2014.04.018
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    1. Christophe Ley & Davy Paindaveine, 2010. "On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 235-250.
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    6. Loperfido, Nicola, 2014. "A note on the fourth cumulant of a finite mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 386-394.
    7. Fujikoshi, Yasunori, 1997. "An Asymptotic Expansion for the Distribution of Hotelling'sT2-Statistic under Nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 187-193, May.
    8. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    9. Giovanni De Luca & Nicola Loperfido, 2015. "Modelling multivariate skewness in financial returns: a SGARCH approach," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1113-1131, November.
    10. Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(5), pages 963-987, October.
    11. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
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    13. Arjun Gupta & Solomon Harrar & Yasunori Fujikoshi, 2008. "MANOVA for large hypothesis degrees of freedom under non-normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 120-137, May.
    14. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Loperfido, Nicola, 2020. "Some remarks on Koziol’s kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    2. Loperfido, Nicola, 2015. "Vector-valued skewness for model-based clustering," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 230-237.
    3. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    4. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    5. Nicola Loperfido & Tomer Shushi, 2023. "Optimal Portfolio Projections for Skew-Elliptically Distributed Portfolio Returns," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 143-166, October.
    6. 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.
    7. Nicola Loperfido, 2023. "Kurtosis removal for data pre-processing," 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. 17(1), pages 239-267, March.

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