Likelihood-based inference for multivariate extreme-value models is often unreliable or infeasible when likelihoods are intractable or supports are discrete. This challenge is particularly acute for multivariate discrete generalized Pareto models, where both marginal tail behavior and dependence must be inferred from sparse exceedance samples. We propose a two-stage likelihood-free inference procedure, termed AW--NBE (Adaptive Wasserstein Neural Bayes Estimator), that combines neural Bayes estimation with a targeted optimal transport refinement step based on the Sinkhorn discrepancy. In the first stage, a neural Bayes estimator trained on simulated data provides fast and stable initial parameter estimates. In the second stage, these estimates are locally refined by minimizing the Sinkhorn divergence between the empirical distributions of observed and simulated exceedances. This refinement reduces the Sinkhorn discrepancy between the empirical distributions of observed and simulated exceedances, while preserving dependence features learned by the neural estimator. Model adequacy is assessed using new optimal transport based multivariate Q--Q and potential diagnostics. Applications to financial log-returns and Swiss dry spell exceedances suggest that AW--NBE can improve parameter inferences compared to estimation using solely, either the Sinkhorn discrepancy, or the standard neural Bayes estimators and censored likelihood estimation.

翻译：基于似然的多元极值模型推断在似然函数不可解或支撑集离散时往往不可靠或不可行。这一挑战在多元离散广义帕累托模型中尤为突出，因为此时必须从稀疏的超阈值样本中同时推断边际尾部行为与相依结构。我们提出一种两阶段免似然推断程序，命名为AW--NBE（自适应Wasserstein神经贝叶斯估计器），该方法将神经贝叶斯估计与基于Sinkhorn散度的目标最优传输精化步骤相结合。第一阶段，在模拟数据上训练的神经贝叶斯估计器提供快速稳定的初始参数估计；第二阶段，通过最小化观测超阈值与模拟超阈值经验分布之间的Sinkhorn散度，对初始估计进行局部精化。该精化过程在降低观测与模拟超阈值经验分布之间Sinkhorn散度的同时，保留神经估计器习得的相依结构特征。模型充分性检验采用基于最优传输的新多元Q-Q图与势诊断方法。金融对数收益率与瑞士干旱持续时间超阈值应用表明，相较于单独使用Sinkhorn散度、标准神经贝叶斯估计器或截断似然估计，AW--NBE能够改善参数推断效果。