Expert mixture models based on extended skew-normal distributions for financial data analysis

Hashemi, Farzane

doi:10.22034/jirss.2026.2081234.1170

Expert mixture models based on extended skew-normal distributions for financial data analysis

Articles in Press

Document Type : Original Article

Author

Farzane Hashemi

Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.

10.22034/jirss.2026.2081234.1170

Abstract

The mixture-of-experts (MoE) framework provides a flexible probabilistic approach for modeling, classification, and clustering of heterogeneous data by combining several local expert models under a gating mechanism. Each expert specializes in a subset of the input space, while the gating function determines the data-to-expert allocation through covariate-dependent mixing proportions. Although the classical MoE formulation-typically assuming normally distributed error terms-offers analytical convenience, it often lacks robustness when data exhibit asymmetry, heavy tails, or contamination. To overcome these challenges, we propose a novel robust nonnormal MoE model in which each expert component follows a log scale-shape mixture of skew-normal (SSMSN) distribution. This formulation, belonging to the broader SSMSN family, allows the model to flexibly capture skewed and heavy-tailed behaviors that frequently arise in economic and financial datasets. To efficiently estimate the model parameters, we propose an Expectation-Maximization (EM) algorithm that maximizes the likelihood function to obtain the maximum likelihood (ML) estimates. We conduct extensive Monte Carlo simulations to assess the finite-sample properties, robustness, and accuracy of the proposed estimator. Finally, the practical usefulness of the proposed MoE-SSMSN framework is demonstrated through an empirical application to real data analysis, highlighting its superiority in modeling heterogeneous, and skewed observations.

Keywords

Mixture of experts

Scale-shape mixture of skew normal

Robust estimation

Heavy-tailed data

Financial modeling

Subjects

Statistical Modelling

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