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Dimension-wise scaled normal mixtures with application to finance and biometry

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  • Punzo, Antonio
  • Bagnato, Luca

Abstract

We propose the family of dimension-wise scaled normal mixtures (DSNMs) to model the joint distribution of a d-variate random variable with real-valued components. Each member of the family generalizes the multivariate normal (MN) distribution in two directions. Firstly, the DSNM has a more general type of symmetry with respect to the elliptical symmetry of the MN distribution. Secondly, the univariate marginals have similar heavy-tailed normal scale mixture distributions with (possibly) different tailedness parameters; as a consequence of practical interest, the DSNM allows for a different excess kurtosis on each dimension. These peculiarities are obtained in an MN scale mixture framework by introducing a d-variate mixing random variable with independent and similar components acting separately for each dimension. We examine several properties of DSNMs, such as the joint density function, hierarchical and stochastic representations, relations with other families of symmetric distributions, type of symmetry, marginal and conditional distributions, no correlation implying independence, moment generating function, and moments of practical interest. For illustrative purposes, we describe two members of the DSNM family obtained in the case of components of the mixing random vector being either uniform or shifted exponential; these are examples of mixing distributions that guarantee a closed-form expression for the joint density of the DSNM. For the two DSNMs analyzed in detail, we introduce parsimony by allowing the d tailedness parameters to be tied across dimensions, and describe algorithms, based on the expectation–maximization (EM) principle, to estimate the parameters by maximum likelihood. We use real data from the financial and biometrical fields to appreciate the advantages of our DSNMs over other symmetric heavy-tailed distributions available in the literature.

Suggested Citation

  • Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
  • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000434
    DOI: 10.1016/j.jmva.2022.105020
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    References listed on IDEAS

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    1. Lee, Lung-Fei, 1983. "The determination of moments of the doubly truncated multivariate normal tobit model," Economics Letters, Elsevier, vol. 11(3), pages 245-250.
    2. Kojadinovic, Ivan, 2017. "Some copula inference procedures adapted to the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 24-41.
    3. Hui, Wallace & Gel, Yulia R. & Gastwirth, Joseph L., 2008. "lawstat: An R Package for Law, Public Policy and Biostatistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i03).
    4. Melnykov, Volodymyr & Zhu, Xuwen, 2018. "On model-based clustering of skewed matrix data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 181-194.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    6. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    7. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    8. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, October.
    9. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    10. Luca Bagnato & Antonio Punzo, 2021. "Unconstrained representation of orthogonal matrices with application to common principal components," Computational Statistics, Springer, vol. 36(2), pages 1177-1195, June.
    11. Manzotti, A. & Pérez, Francisco J. & Quiroz, Adolfo J., 2002. "A Statistic for Testing the Null Hypothesis of Elliptical Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 274-285, May.
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