Limit Theorem for Kernel Estimate of the Conditional Hazard Function with Weakly Dependent Functional Data

This paper investigates the asymptotic behavior of the conditional hazard function by kernel method , with particular focus on functional weakly dependent data. Specifically, we establish the asymptotic normality for the proposed estimator when the covariate be a functional quasi-associated process. This result contributes to the broader framework of nonparametric inference under weak dependence and functional data analysis. The estimator is constructed using kernel smoothing techniques inspired by the classical Nadaraya-Watson approach, and its theoretical properties are rigorously derived under suitable regularity conditions. To assess its practical performance, we carry out an extensive simulation study, comparing finite-sample results to their asymptotic counterparts. The findings demonstrate the robustness and reliability of the estimator across various settings, confirming the validity of the stated limit theorem in empirical contexts.