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

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 non-normal 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.