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Matrix-variate normal mean-variance Birnbaum–Saunders distributions and related mixture models

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  • Salvatore D. Tomarchio

    (Università degli Studi di Catania)

Abstract

Matrix-variate data analysis has increasingly attracted interest in the statistical literature over the recent years, especially in the model-based clustering framework. Here, we firstly introduce a new matrix-variate skewed distribution: the matrix-variate normal mean-variance Birnbaum–Saunders distribution. Then, we obtain its symmetric version by constraining the skewness matrix to be a matrix of zeros. Both distributions are then used as components of the corresponding mixture models and used for model-based clustering. Two ECM algorithms are proposed for parameter estimation. By using simulated analyses, we investigate the parameter recovery of our ECM algorithms and the performance of different initialization strategies for our mixture models on several scenarios and under different points of view. Then, our models are compared to other competitors via simulated data as well as in two real data applications.

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  • Salvatore D. Tomarchio, 2024. "Matrix-variate normal mean-variance Birnbaum–Saunders distributions and related mixture models," Computational Statistics, Springer, vol. 39(2), pages 405-432, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01290-9
    DOI: 10.1007/s00180-022-01290-9
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    References listed on IDEAS

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    1. Gallaugher, Michael P.B. & McNicholas, Paul D., 2019. "Three skewed matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 103-109.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Laura Anderlucci & Angela Montanari & Cinzia Viroli, 2014. "A Matrix-Variate Regression Model with Canonical States: An Application to Elderly Danish Twins," Statistica, Department of Statistics, University of Bologna, vol. 74(4), pages 367-381.
    4. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
    5. Sarkar, Shuchismita & Zhu, Xuwen & Melnykov, Volodymyr & Ingrassia, Salvatore, 2020. "On parsimonious models for modeling matrix data," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    6. Michael P. B. Gallaugher & Paul D. McNicholas, 2020. "Mixtures of skewed matrix variate bilinear factor analyzers," 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. 14(2), pages 415-434, June.
    7. Farzane Hashemi & Mehrdad Naderi & Ahad Jamalizadeh & Tsung-I Lin, 2020. "A skew factor analysis model based on the normal mean–variance mixture of Birnbaum–Saunders distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(16), pages 3007-3029, December.
    8. Tomarchio, Salvatore D. & Punzo, Antonio & Bagnato, Luca, 2020. "Two new matrix-variate distributions with application in model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    9. Semhar Michael & Volodymyr Melnykov, 2016. "An effective strategy for initializing the EM algorithm in finite mixture models," 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. 10(4), pages 563-583, December.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
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