Extreme Quantile Regression: Estimation and Model Selection

Abstract

Extreme quantile regression is a statistical method that focuses on estimating conditional quantiles in the tails of a distribution. Solving such problems requires tools from statistics, extreme value theory, optimization and is particularly relevant in high-dimensional settings, such as finance and health care. The objective of this thesis is to develop and evaluate methodologies for extreme quantile regression in high-dimensional contexts. To achieve this, we first review existing methods for solving penalized linear regression and quantile regression problems and then build on this foundation to extend penalization to extreme quantile regression.