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A Laplace-based model with flexible tail behavior

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  • Tortora, Cristina
  • Franczak, Brian C.
  • Bagnato, Luca
  • Punzo, Antonio

Abstract

The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate asymmetric Laplace distribution to allow for a different excess kurtosis on each dimension and for more flexible shapes of the hyper-contours. These peculiarities are obtained by working on the principal component (PC) space. The structure of the MSCAL distribution has the further advantage of allowing for automatic PC-wise outlier detection – i.e., detection of outliers separately on each PC – when convenient constraints on the parameters are imposed. The MSCAL is fitted using a Monte Carlo expectation-maximization (MCEM) algorithm that uses a Monte Carlo method to estimate the orthogonal matrix of eigenvectors. A simulation study is used to assess the proposed MCEM in terms of computational efficiency and parameter recovery. In a real data application, the MSCAL is fitted to a real data set containing the anthropometric measurements of monozygotic/dizygotic twins. Both a skewed bivariate subset of the full data, perturbed by some outlying points, and the full data are considered.

Suggested Citation

  • Tortora, Cristina & Franczak, Brian C. & Bagnato, Luca & Punzo, Antonio, 2024. "A Laplace-based model with flexible tail behavior," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002207
    DOI: 10.1016/j.csda.2023.107909
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    References listed on IDEAS

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    8. 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.
    9. Salvatore D. Tomarchio & Antonio Punzo, 2020. "Dichotomous unimodal compound models: application to the distribution of insurance losses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2328-2353, November.
    10. Francesca Greselin & Antonio Punzo, 2013. "Closed Likelihood Ratio Testing Procedures to Assess Similarity of Covariance Matrices," The American Statistician, Taylor & Francis Journals, vol. 67(3), pages 117-128, August.
    11. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
    12. Punzo, Antonio & Bagnato, Luca, 2021. "Modeling the cryptocurrency return distribution via Laplace scale mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    13. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
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