Partially linear models (PLMs) are widely employed in scientific research to analyze hybrid parametric-nonparametric relationships. However, their conventional reliance on symmetric error distributions severely limits applicability to real-world phenomena characterized by pronounced asymmetry and heavy-tailed behavior. To address this gap, we propose a novel PLM framework incorporating skewed generalized normal (SGN) distributed errors, which simultaneously accommodates extreme skewness and heavy-tailed attributes beyond the capabilities of symmetric or skew-normal (SN) specifications. Methodologically, we develop a penalized expectation-maximization (EM) algorithm with provable convergence guarantees and integrated adaptive smoothing selection, effectively resolving optimization instability in high-dimensional settings. Furthermore, we establish a unified diagnostic system that synergizes geometric leverage calculus with local influence analysis to systematically evaluate model robustness against perturbations and outliers. Extensive simulation studies demonstrate the framework's superior estimation accuracy compared to conventional symmetric and SN-based alternatives. Empirical validations based on real-world datasets reveal statistically significant improvements in model fit while maintaining interpretability.

In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis.