Maximum Likelihood Estimation in Shape and Skew Scale Mixtures of Normal Linear Regression Models: The Impact of Reparameterization

Articles in Press

Document Type : Original Article

Authors
Zakaria Alizadeh Ghajari 1
Karim Zare 1
Soheil Shokri 2
Abdul Rasoul Ziaei 3
1 Department of Statistics, Marv.C., Islamic Azad University, Marvdasht, Iran
2 Department of Statistics, Ra.C., Islamic Azad University, Rasht, Iran
3 Department of Statistics, Das.C., Islamic Azad University, Borazjan, Iran
10.22034/jirss.2026.2085508.1184
Abstract
This study introduces a novel class of Linear Regression Models (LRM), the Shape and Skew Scale Mixtures of Normal (SHSSMN) distributions, to effectively handle skewed and heavy-tailed error terms. By extending the Expectation-Maximization (EM) algorithm, we explore two distinct scenarios based on without or with reparametrization. Simulation results demonstrate that the parameter estimates under both scenarios are consistent and nearly identical, with the second scenario offering a computational advantage by reducing the number of iterations required for convergence, especially for complex distributions. The models are applied to real-world data from the Australian Institute of Sport (AIS) to evaluate their practical utility. The results show that the SHSSMN models, particularly the Modified Skew-t Cauchy (STC) distribution, provide superior fit and effectively address the skewness and heavy-tailed nature of the residuals, making them a valuable tool for regression analysis in diverse fields.
Keywords
EM-type algorithm
Linear regression models
Monte Carlo simulation
Shape and skew scale mixtures of normal distributions
Subjects
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Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 02 August 2026

  • Receive Date 15 February 2026
  • Revise Date 10 July 2026
  • Accept Date 25 July 2026