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The kurtosis coeficient and the linear discriminant function

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  • Prieto, Francisco J.

Abstract

In this note we analyze the relationship between the direction obtained from the minimization of the kurtosis coefficient of the projections of a mixture of multivariate normal distributions and the linear discriminant function. We show that both directions are closely related, and in particular that given two vector random variables having symmetric distributions with unknown means and the same covariance matrix,the direction which minimizes the kurtosis coefficient of the projection is the linear discriminant function. This result provides a way to compute the discriminant function between two normal populations in the case in which the means and the common covariance matrix are unknown.

Suggested Citation

  • Prieto, Francisco J., 1999. "The kurtosis coeficient and the linear discriminant function," DES - Working Papers. Statistics and Econometrics. WS 6358, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6358
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    Cited by:

    1. Loperfido, Nicola, 2015. "Vector-valued skewness for model-based clustering," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 230-237.
    2. Salem Reyen & John Miller & Edward Wegman, 2009. "Separating a mixture of two normals with proportional covariances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 297-314, November.
    3. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    4. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    5. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    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. 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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