Expert Kaplan--Meier estimation

TL;DR

This paper enhances Kaplan--Meier estimation in right-censored data by integrating expert knowledge to address contamination, providing consistency results and practical illustrations with insurance data.

Contribution

It introduces two novel methods for incorporating expert information into the Kaplan--Meier estimator, with theoretical consistency proofs and practical applications.

Findings

Strong uniform consistency established for both methods.

Techniques applicable under specific contamination and expert knowledge assumptions.

Illustrations demonstrate effectiveness on simulated and real insurance data.

Abstract

The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the product-limit estimator in two different ways with distinct interpretations. Strong uniform consistency is proved for both cases under certain assumptions on the kind of contamination and the quality of expert information, which sheds light on the techniques and decisions that practitioners may take. The nuances of the techniques are discussed -- also with a view towards semi-parametric estimation -- and they are illustrated using simulated and real-world insurance data.