We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of extrapolating extreme values. Given the scarcity of extreme events, we argue that a simple, robust modeling approach is essential. We adopt univariate models instead of multivariate ones and model Peaks Over Thresholds using Extreme Value Theory. Specifically, we fit an exponential distribution to model exceedances of the target variable above a high quantile (after seasonal adjustment). The novelty of our approach lies in using martingale testing to evaluate the extrapolation power of the procedure and to agnostically select the level of the high quantile. While this method has several limitations, we believe that framing extrapolation as a game opens the door to other agnostic approaches in Extreme Value Analysis.

翻译：我们提出了EVA2025数据挑战赛的获胜策略，该挑战旨在估计极端降水事件的概率。这些事件在数据集中最多只发生一次，使得该挑战本质上成为一个极值外推问题。鉴于极端事件的稀缺性，我们认为采用简单、稳健的建模方法至关重要。我们选择单变量模型而非多变量模型，并利用极值理论对超阈值峰值进行建模。具体而言，我们拟合指数分布来模拟经过季节性调整后目标变量超过高分位数的部分。本方法的新颖之处在于利用鞅检验来评估该过程的推断能力，并基于无偏原则选择高分位数的水平。尽管该方法存在若干局限性，但我们相信将推断问题框架化为博弈过程，为极值分析中其他无偏方法的探索开辟了道路。