Asymptotic normality of adaptive recursive kernel estimator of the density in a right censored model

This result focuses on the asymptotic properties of an adaptive recursive kernel density estimator for independent right-censored data. We establish asymptotic normality under regularity condition. As an application, we construct asymptotic confidence intervals for the unknown lifetime density function. The theoretical results are supported by a detailed simulation study, illustrating the estimator’s accuracy, efficiency, and robustness in practical settings.