Gini Score under Ties and Case Weights

TL;DR

This paper explores how to adapt the Gini score for risk ranking when ties occur and case weights are present, extending its applicability in actuarial and statistical modeling contexts.

Contribution

It introduces methods to handle ties and case weights in the Gini score, broadening its use beyond binary and continuous risk rankings.

Findings

Gini score can be effectively adapted for tied risk rankings.

Incorporating case weights improves the accuracy of the Gini score.

Extensions enable the Gini score's use in more complex actuarial models.

Abstract

The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has mainly been used in a binary context, in which it has many equivalent reformulations such as the receiver operating characteristic (ROC) or the area under the curve (AUC). In the actuarial literature, this rank based score for binary responses has been extended to general real-valued random variables using Lorenz curves and concentration curves. While these initial concepts assume that the risk ranking is generated by a continuous distribution function, we discuss in this paper how the Gini score can be used in the case of ties in the risk ranking. Moreover, we adapt the Gini score to the common actuarial situation of having case weights.