Tail index partition-based rules extraction with application to tornado damage insurance

The tail index is an important parameter that measures how extreme events occur. In many practical cases, this tail index depends on covariates. In this paper,we assume that it takes a finite number of values over a partition of the covariate space. This article proposes a tail index partition-based rules extraction method that is able to construct estimates of the partition subsets and estimates of the tail index values. The method combines two steps: first an additive tree ensemble based on the Gamma deviance is fitted, and second a hierarchical clustering with spatial constraints is used to estimate the subsets of the partition. We also propose a global tree surrogate model to approximate the partition-based rules while providing an explainable model from the initial covariates. Our procedure is illustrated on simulated data. A real case study on wind property damages caused by tornadoes is finally presented.

Automated summary

This paper proposes a tail index partition-based rules extraction method that can construct estimates of the partition subsets and estimates of the tail index values. The method includes fitting an additive tree ensemble based on the Gamma deviance and using hierarchical clustering with spatial constraints to estimate the subsets of the partition. A global tree surrogate model is also proposed to approximate the partition-based rules while providing an explainable model from the initial covariates. The procedure is illustrated on simulated data and a real case study on wind property damages caused by tornadoes.