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A note on the fourth cumulant of a finite mixture distribution

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  • Loperfido, Nicola

Abstract

The paper shows that the fourth cumulant of a finite mixture distribution might be decomposed into the mean of the components’ fourth cumulants and the fourth cumulant of the components’ means, when the mixture’s components have the same second and third cumulants. Statistical applications include robustness properties of likelihood-based testing procedures and kurtosis-based projection methods. Practical relevance of theoretical results in the paper are illustrated with two well-known data sets.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:386-394
    DOI: 10.1016/j.jmva.2013.09.007
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    References listed on IDEAS

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    Cited by:

    1. Jorge M. Arevalillo & Hilario Navarro, 2021. "Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    2. Javed, Farrukh & Loperfido, Nicola & Mazur, Stepan, 2024. "Edgeworth expansions for multivariate random sums," Econometrics and Statistics, Elsevier, vol. 31(C), pages 66-80.
    3. Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.
    4. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).

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