Publication Date
5-11-2026
Document Type
Article
Publication Title
Computational Statistics
Volume
41
Issue
4
DOI
10.1007/s00180-026-01751-5
Abstract
Handling missing data is a major challenge in model-based clustering, especially when the data exhibit skewness and heavy tails. We address this by extending the finite mixture of scale mixtures of multivariate skew-normal (FMSMSN) family to accommodate incomplete data under a missing at random (MAR) mechanism. Unlike previous work that is limited to one of the special cases of the FMSMSN family, our method offers a cluster analysis methodology for the entire family that accounts for skewness and excess kurtosis amidst data with missing values. The multivariate skew-normal distribution, as parameterised by Azzalini and Dalla Valle (Biometrika 83(4):715–726, 1996) and Arnold and Beaver (Test 11:7–54, 2002), includes the normal distribution as a special case, which ensures that our method is flexible toward existing symmetric model-based clustering techniques under a normality assumption. We derive the distributional properties of the missing components of the data and propose an EM-type algorithm tailored for incomplete observations. The modified E-step yields closed-form expressions for the conditional expectations of the missing values. The simulation experiments showcase the flexibility of the FMSMSN family in both clustering performance and parameter recovery for varying percentages of missing values, while incorporating the effects of sample size and cluster proximity. Finally, we illustrate the practical utility of the proposed method by applying special cases of the FMSMSN family to global CO2 emissions data.
Funding Number
RA231117164450
Funding Sponsor
National Research Foundation of Korea
Keywords
EM algorithm, Missing values, Mixture models, Scale mixtures, Skewness
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Jason Pillay, Cristina Tortora, Antonio Punzo, and Andriette Bekker. "Clustering data with values missing at random using scale mixtures of multivariate skew-normal distributions" Computational Statistics (2026). https://doi.org/10.1007/s00180-026-01751-5
