Nonparametric Survival Estimation with Contaminated and Adjudicated Events

TL;DR

This paper extends the Kaplan-Meier estimator to handle contaminated event data with expert adjudication, providing asymptotic theory, bias analysis, and practical applications in credit risk.

Contribution

It introduces a comprehensive asymptotic framework for the conditional expert Kaplan-Meier estimator incorporating covariates and contamination effects.

Findings

Unbiased expert judgments ensure estimator consistency.

Systematic expert bias induces a quantifiable asymptotic bias.

Simulation studies demonstrate finite-sample performance and practical utility.

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.