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

2025-12-16

AI Summary

This paper addresses the modeling challenge of survival data exhibiting both right-censoring and expert judgment contamination—common in insurance and credit risk applications. We propose a covariate-dependent conditional expert Kaplan–Meier estimator. Our work establishes, for the first time under contamination, the functional consistency and weak convergence theory for conditional survival function estimation; it rigorously characterizes the asymptotic bias induced by systematic expert deviation and provides an analytically explicit bias-correction formula. Theoretically, the estimator is strongly consistent under unbiased expert judgments, while under systematic bias, it exhibits a deterministic asymptotic bias that admits precise characterization. Through kernel smoothing, empirical process techniques, and Monte Carlo simulations, we demonstrate that the estimator achieves superior robustness and practical performance on both synthetic data and real-world loan default datasets.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Applications
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Security and Privacy: Large-scale security measurements

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.

Problem

• Estimates time-to-event data with right-censoring and contamination
• Incorporates covariates via kernel smoothing for conditional estimation
• Quantifies bias from imperfect expert judgments in loan default modeling

Innovation

• Conditional expert Kaplan-Meier estimator with covariates
• Kernel smoothing for incorporating covariate information
• Asymptotic theory for bias from imperfect expert judgments