In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed using extreme value theory. We consider the popular peaks over a threshold method and show that the generalised Pareto approximation of the true predictive densities of both a future unobservable excess or peak random variable can be very accurate. We propose both a frequentist and a Bayesian approach for the estimation of such predictive densities. We show the asymptotic accuracy of the corresponding estimators and, more importantly, prove that the resulting predictive inference is asymptotically reliable. We show the utility of the proposed predictive tools analysing extreme temperatures in Milan in Italy.

翻译：在许多应用领域中，需要做出预测以评估比已记录事件更严重事件的可能性，从而防范尚未发生的灾难。该问题可利用极值理论进行分析。我们考虑流行的阈值超出峰方法，并证明广义帕累托近似对于未来不可观测的超额变量或峰值随机变量的真实预测密度可以非常精确。我们提出了频率学派和贝叶斯两种方法来估计此类预测密度。我们证明了相应估计量的渐近准确性，更重要的是，证明了由此产生的预测推断在渐近意义上是可靠的。通过分析意大利米兰的极端温度数据，我们展示了所提出预测工具的有效性。