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A Laplace-based model with flexible tail behavior

Faculty Advisor

Date

2024

Keywords

contaminated distributions, directional outlier detection, Monte Carlo expectation-maximization algorithm, multiple scaled distributions, normal variance-mean mixtures

Abstract (summary)

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.

Publication Information

Tortora C., Franczak B. C., Bagnato, L., & Punzo A. (2024) A Laplace-based model with flexible tail behavior. Computational Statistics and Data Analysis, 192, 107909. https://doi.org/10.1016/j.csda.2023.107909

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Article

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Rights

Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)