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Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions

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  • Morris, Katherine
  • Punzo, Antonio
  • McNicholas, Paul D.
  • Browne, Ryan P.

Abstract

Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related non-contaminated mixture, for each (asymmetric) cluster, our model has one parameter controlling the proportion of outliers and another specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach that is absent from other approaches such as trimming. Moreover, each observation is given an a posteriori probability of belonging to a particular cluster, and of being an outlier or not; advantageously, this allows for the automatic detection of outliers. An expectation–conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. The behavior of the proposed model is investigated, and compared with well-established finite mixture approaches, on artificial and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:132:y:2019:i:c:p:145-166
    DOI: 10.1016/j.csda.2018.12.001
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    5. Amovin-Assagba, Martial & Gannaz, Irène & Jacques, Julien, 2022. "Outlier detection in multivariate functional data through a contaminated mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Ryan P. Browne & Luca Bagnato & Antonio Punzo, 2024. "Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions," 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. 18(3), pages 597-625, September.
    7. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    8. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    9. 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).

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