In the extreme value theory domain, can you explain visually what is needed to select the right threshold using the peak over threshold approach when having a low sample size?

视频信息

答案文本 复制

视频字幕 复制

Extreme Value Theory is used to model rare events that occur with low probability but high impact. The Peak Over Threshold approach is a common method where we select a threshold and model only the values that exceed it using a Generalized Pareto Distribution. The key challenge, especially with limited data, is selecting the right threshold. If the threshold is too low, we include non-extreme data, leading to biased estimates. If it's too high, we have too few exceedances, resulting in high variance. With small sample sizes, this trade-off becomes even more critical.