Informed censoring: the parametric combination of data and expert information

TL;DR

This paper introduces a new statistical framework called informed censoring that combines data and expert information for improved parametric estimation, with theoretical backing and practical actuarial applications.

Contribution

It develops a novel methodology for integrating expert information into censoring models, extending traditional methods and providing asymptotic theory for the estimators.

Findings

The framework generalizes censoring and coarsening at random.

Asymptotic properties of the estimators are established.

Application to tail parameter estimation in heavy-tailed datasets demonstrates practical utility.

Abstract

The statistical censoring setup is extended to the situation when random measures can be assigned to the realization of datapoints, leading to a new way of incorporating expert information into the usual parametric estimation procedures. The asymptotic theory is provided for the resulting estimators, and some special cases of practical relevance are studied in more detail. Although the proposed framework mathematically generalizes censoring and coarsening at random, and borrows techniques from M-estimation theory, it provides a novel and transparent methodology which enjoys significant practical applicability in situations where expert information is present. The potential of the approach is illustrated by a concrete actuarial application of tail parameter estimation for a heavy-tailed MTPL dataset with limited available expert information.