Semiparametric Inference for Functional Survival Models

In recent years, there has been growing interest among researchers in modeling right-censored survival data with functional covariates.While existing functional methods primarily focus on the Cox model, its proportional hazards assumption can be challenging to verify and may be violated in practice.To address this issue, we extend the ordinary differential equation (ODE) framework for survival data to incorporate functional covariates and develop an inference procedure for both scalar and functional parameters.Specifically, we establish asymptotic normality and semiparametric efficiency for the scalar coefficient estimators, enabling a valid inference procedure.Additionally, we derive an asymptotic simultaneous confidence band for the functional parameter.Simulations are conducted to evaluate the finite sample performance of the proposed method.