Alternative Cholesky Decomposition and family of scale mixture of Normal distribution: A joint modeling approach - Ribeiro, Vinícius Silva Osterne; Bombrun, Lionel; Nobre, Juvêncio Santos; Cavalcante, Charles Casimiro; Berthoumieu, Yannick (Signal processing, 2026)
In Statistics, the analysis of longitudinal data is essential across various domains, including biomedical and agricultural research. Joint mean-covariance models have been widely used to capture within-subject dependence, often by parametrizing the scatter matrix via the Modified Cholesky Decomposition (MCD). However, the MCD has known drawbacks, such as sensitivity to the ordering of variables and challenges in parameter interpretation. As an alternative, the Alternative Cholesky Decomposition (ACD) offers improved numerical stability and interpretability, yet has been underexplored in robust modeling contexts. Traditional approaches also frequently assume normally distributed residuals, which may not hold in practice. While extensions based on the Student-t and Laplace distributions address heavier tails, they still rely on fixed parametric forms. To overcome both structural and distributional limitations, this paper proposes a novel joint regression model that combines the flexibility of ACD with the robustness of scale mixture of normal (SMN) distributions. We obtain maximum likelihood estimators and compare our model against classical and Student-t-based alternatives. Simulation studies show superior performance in estimation and prediction under outlier contamination. Real data applications further highlight the model’s robustness and practical utility.