Model Selection and Diagnostics in Extreme Value Theory

Model selection and diagnostic testing are critical components in applying Extreme Value Theory (EVT) for real-world data analysis. EVT models, such as the Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD), are used to estimate the behavior of extreme events, but selecting the appropriate model and evaluating its fit to the data are essential steps for reliable predictions. This paper discusses various model selection methods, including goodness-of-fit tests, crossvalidation techniques, and model comparison criteria like Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC). Additionally, diagnostic tools such as quantile-quantile (Q-Q) plots, probability-probability (P-P) plots, and residual analysis are explored to assess the adequacy of EVT models. The article emphasizes the importance of robust diagnostic procedures to ensure that the chosen model accurately captures the tail behavior of the data