Robust semi-functional censored regression

This paper develops a robust methodological framework for analyzing randomly censored responses within the semi-functional partial linear regression models, utilizing the exponential squared loss criterion. The proposed methodology capitalizes on the robustness of the exponential squared loss function against outliers and heavy-tailed error distributions, while preserving the flexibility and interpretability of semi-functional regression, which accommodates scalar and functional predictors in a unified framework. To account for the divergent convergence rates of the parametric and nonparametric components, we introduce a novel three-step estimation procedure designed to enhance computational efficiency, ensure model robustness, and achieve asymptotically optimal estimation performance. The parametric component is estimated through a quasi-Newton algorithm, for which we establish global convergence under standard regularity conditions using a Wolfe-type line search strategy. Additionally, we suggest a cross-validation criterion based on the exponential squared loss function to guide the data-driven selection of tuning parameters. The theoretical properties, including consistency and asymptotic normality of the proposed estimators, are established under mild conditions. The efficacy and robustness of the method are demonstrated through a series of simulation studies and an empirical application to Alzheimer’s disease progression, highlighting its practical applicability in addressing complex and censored data structures.