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Manly transformation in finite mixture modeling

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  • Zhu, Xuwen
  • Melnykov, Volodymyr

Abstract

Finite mixture modeling is one of the most rapidly developing areas of statistics due to its modeling flexibility and appealing interpretability. Gaussian mixture models have been popular among researchers for decades proving their usefulness in various applications. However, when Gaussian mixture components do not provide an adequate fit for the data, more general models must be considered. Traditional remedies for deviation from normality include employing a more appropriate distribution as well as transforming data to near-normality. Merging both approaches by introducing a mixture model with components derived from the multivariate Manly transformation is proposed. Such mixture models show good performance in modeling skewness and have excellent interpretability. Forward and backward model selection algorithms are proposed to choose an appropriate multivariate transformation. At each step of these algorithms, a model with the specific combination of skewness parameters is estimated by means of the expectation–maximization algorithm. The developed technique is carefully illustrated on synthetic data and applied to several well-known datasets, with promising results.

Suggested Citation

  • Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:190-208
    DOI: 10.1016/j.csda.2016.01.015
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    References listed on IDEAS

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    2. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Yana Melnykov & Marcus Perry, 2024. "On Robust Change Point Detection and Estimation in Multisubject Studies," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 827-879, August.
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    5. Yingqiu Zhu & Qiong Deng & Danyang Huang & Bingyi Jing & Bo Zhang, 2021. "Clustering based on Kolmogorov–Smirnov statistic with application to bank card transaction data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 558-578, June.
    6. Volodymyr Melnykov & Xuwen Zhu, 2019. "Studying crime trends in the USA over the years 2000–2012," 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. 13(1), pages 325-341, March.
    7. Shuchismita Sarkar & Volodymyr Melnykov & Rong Zheng, 2020. "Gaussian mixture modeling and model-based clustering under measurement inconsistency," 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 379-413, June.
    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. Puneet Prakash & Vikas Sangwan & Kewal Singh, 2021. "Transformational Approach to Analytical Value-at-Risk for near Normal Distributions," JRFM, MDPI, vol. 14(2), pages 1-19, January.
    10. Melnykov, Volodymyr & Zhu, Xuwen, 2018. "On model-based clustering of skewed matrix data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 181-194.

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