Extreme value statistics using related variables

This dissertation contains five chapters that involve the use of the extreme value theory. Chapter 2 provides a novel methodology for improving the extreme value index estimation based on covariates in the case of heavy-tailed distributions. An application of the earthquakes and the related financial losses is used to show the improvement obtained when applying the proposed methodology. Chapters 3 and 4 introduce further generalizations for the proposed methodology in Chapter 2, by considering less assumptions, all cases for the extreme value index, and extending to the scale parameter and the estimation of the extreme quantile. In Chapter 3, An application of rainfall in France is used to demonstrate the use of the generalized methodology introduced in these two chapters. Chapter 5 combines the use of the extreme value theory with machine learning techniques. In Chapter 5, the machine learning technique is used to obtain an estimator of the Value-at-Risk (VaR) based on related covariates. An insurance application is used to show the effectiveness of the combined methodology of extreme value theory with machine learning.