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Mixtures of multivariate contaminated normal regression models

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  • Angelo Mazza

    (University of Catania)

  • Antonio Punzo

    (University of Catania)

Abstract

Mixtures of regression models (MRMs) are widely used to investigate the relationship between variables coming from several unknown latent homogeneous groups. Usually, the conditional distribution of the response in each mixture component is assumed to be (multivariate) normal (MN-MRM). To robustify the approach with respect to possible elliptical heavy-tailed departures from normality, due to the presence of mild outliers, the multivariate contaminated normal MRM is here introduced. In addition to the parameters of the MN-MRM, each mixture component has a parameter controlling the proportion of outliers and one specifying the degree of contamination with respect to the response variable(s). Crucially, these parameters do not have to be specified a priori, adding flexibility to our approach. Furthermore, once the model is estimated and the observations are assigned to the groups, a finer intra-group classification in typical points and (mild) outliers, can be directly obtained. Identifiability conditions are provided, an expectation-conditional maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments and compared with other procedures. The performance of this novel family of models is also illustrated on artificial and real data, with particular emphasis to the application in allometric studies.

Suggested Citation

  • Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0964-y
    DOI: 10.1007/s00362-017-0964-y
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    Cited by:

    1. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    2. 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.
    3. Gabriele Perrone & Gabriele Soffritti, 2023. "Seemingly unrelated clusterwise linear regression for contaminated data," Statistical Papers, Springer, vol. 64(3), pages 883-921, June.
    4. Katerina Arnostova & Tomas Adam & Oxana Babecka Kucharcukova & Jan Babecky & Vojtech Belling & Sona Benecka & Jan Bruha & Martin Gurtler & Tibor Hledik & Tomas Holub & Eva Hromadkova & Lubos Komarek &, 2017. "Analyses of the Czech Republic's Current Economic Alignment with the Euro Area 2017," Occasional Publications - Edited Volumes, Czech National Bank, number as17 edited by Katerina Arnostova & Lucie Matejkova, January.
    5. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2021. "On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    7. Katerina Arnostova & Oxana Babecka Kucharcukova & Jan Babecky & Vojtech Belling & Sona Benecka & Jan Bruha & Martin Gurtler & Tomas Holub & Eva Hromadkova & Lubos Komarek & Zlatuse Komarkova & Petr Kr, 2016. "Analyses of the Czech Republic's Current Economic Alignment with the Euro Area 2016," Occasional Publications - Edited Volumes, Czech National Bank, number as16 edited by Katerina Arnostova & Lucie Matejkova, January.
    8. Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.

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