Symmetric α -stable distribution for robust semiparametric mixture of regression models

.This article introduces a robust semiparametric mixture of regression (SMR) model utilizing symmetric α-stable (SαS) distribution to address limitations of traditional normal-error SMR frameworks when handling outliers or heavy-tailed data. The proposed model maintains SMR’s core structure with non parametrically estimated mixture weights via kernel density estimation and cluster-specific parametric regressions. The SαS distribution is a generalization of the normal distribution with an additional parameter called α. The normal distribution is obtained when α = 2, and for α < 2, it exhibits heavier tails and unbounded variance, i.e., the variance is infinite when α < 2, thereby providing extreme outlier resilience compared to finite-variance alternatives (e.g., t-distributions with degrees of freedom greater than 2). Parameter estimation employs an expectation-maximization (EM) algorithm for regression coefficients and scale parameters, while α is estimated using Monte Carlo integration and interpolation. Model performance is evaluated against existing mixture regression methods through comprehensive simulations and real-data analyses.