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Moments of scale mixtures of skew-normal distributions and their quadratic forms

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  • Hyoung-Moon Kim
  • Chiwhan Kim

Abstract

We obtain the first four moments of scale mixtures of skew-normal distributions allowing for scale parameters. The first two moments of their quadratic forms are obtained using those moments. Previous studies derived the moments, but all relevant results do not allow for scale parameters. In particular, it is shown that the mean squared error becomes an unbiased estimator of σ2 with skewed and heavy-tailed errors. Two measures of multivariate skewness are calculated.

Suggested Citation

  • Hyoung-Moon Kim & Chiwhan Kim, 2017. "Moments of scale mixtures of skew-normal distributions and their quadratic forms," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1117-1126, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1117-1126
    DOI: 10.1080/03610926.2015.1011339
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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. Jorge M. Arevalillo & Hilario Navarro, 2020. "Data projections by skewness maximization under scale mixtures of skew-normal vectors," 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. 14(2), pages 435-461, June.
    3. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.

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