Conditional Expert Kaplan-Meier Estimation: Asymptotic Theory and an Application to Loan Default Modelling

Abstract: We study the conditional expert Kaplan-Meier estimator, an extension of the classical Kaplan--Meier estimator designed for time-to-event data subject to both right-censoring and contamination. Such contamination, where observed events may not reflect true outcomes, is common in applied settings, including insurance and credit risk, where expert opinion is often used to adjudicate uncertain events. Building on previous work, we develop a comprehensive asymptotic theory for the conditional version incorporating covariates through kernel smoothing. We establish functional consistency and weak convergence under suitable regularity conditions and quantify the bias induced by imperfect expert information. The results show that unbiased expert judgments ensure consistency, while systematic deviations lead to a deterministic asymptotic bias that can be explicitly characterized. We examine finite-sample properties through simulation studies and illustrate the practical use of the estimator with an application to loan default data.