PhD-candidate: Just de Groot
Start: Fall 2025
Extreme values are ubiqutous in the world. Classical inference procedures assume independent and identically distributed data. However, different variables, such as rainfall or age, are subject to external influences in the tails. My research, under Prof. Zhou, focuses on generalising the classical model to allow for inferences on conditional extremes.
Classical methods assume independent and identically distributed data. We model external influences by assuming that, far in the tail, the target variable is aproximately a scale function of the covariates multiplied by an unconditional random variable. The latter dictates the tail heaviness, which is independent of the covariates.
The classical approach utilizes values above a large threshold, known as Peaks over Threshold (POT). The main challenge within our framework is that the threshold is conditional on the covariates. We solve this challenge by providing theoretical guarantees for the quantile regression and maximum likelihood estimators of the POT model.
The research provides a toolkit to derive inferences using extreme value analysis from heterogeneous data, where we allow the endpoint to vary with the covariates. A relevant example would be the extremes of age, which may vary wildly according to external factors. The location and scale of the age of a person may vary as they get closer to the end of their life, and providing valid guarantees for inference becomes all the more important.
