Conditional Quantile Estimation via Conditional Extreme Value Model

Assessing the risk of extreme events is important in fields such as environmental science, finance, and insurance. While univariate extreme value theory (EVT) provides a well-established framework for modeling and extrapolating rare events, the multivariate setting is more challenging under asymptotic independence between variables.

The Heffernan–Tawn (HT) conditional extremes model addresses this by characterizing a response variable’s distribution given that a covariate exceeds a high threshold. However, existing implementations estimate a single pair of location and scale normalizing parameters across the entire covariate space, which limits conditional extreme quantile estimation accuracy where the dependence structure varies across the conditioning space, particularly in data-sparse regions. To address this, the present work proposes a locally adaptive estimator for the HT model based on random-forest-derived adaptive neighbourhoods and weighted quantile regression. The proposed approach preserves the theoretical structure of the conditional extremes model while replacing restrictive global estimation with flexible, locally adaptive inference. 

A simulation study compares the proposed random-forest-weighted (RF) estimator against the global HT benchmark across five bivariate dependence structures spanning asymptotic independence and both strong and weak asymptotic dependence. The RF estimator achieves a consistent RMSE reduction over HT across all structures and target quantile levels ($\tau = 0.90, 0.95, 0.99$). The improvements are particularly pronounced under weak asymptotic dependence and at the most extreme quantile levels.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca.