Publication Date
4-1-2024
Document Type
Article
Publication Title
Computational Statistics and Data Analysis
Volume
192
DOI
10.1016/j.csda.2023.107909
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.
Funding Number
2209974
Funding Sponsor
National Science Foundation
Keywords
Contaminated distributions, Directional outlier detection, Monte Carlo expectation-maximization algorithm, Multiple scaled distributions, Normal variance-mean mixtures
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Department
Mathematics and Statistics
Recommended Citation
Cristina Tortora, Brian C. Franczak, Luca Bagnato, and Antonio Punzo. "A Laplace-based model with flexible tail behavior" Computational Statistics and Data Analysis (2024). https://doi.org/10.1016/j.csda.2023.107909
