Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for this purpose, with L-moment estimation (LME) and maximum likelihood estimation (MLE) being the primary methods. However, estimating high quantiles with a small sample size becomes challenging when the upper endpoint is unbounded, or equivalently, when there are larger uncertainties involved in extrapolation. This study introduces an improved approach using a model averaging (MA) technique. The proposed method combines MLE and LME to construct candidate submodels and assign weights effectively. The properties of the proposed approach are evaluated through Monte Carlo simulations and an application to maximum daily rainfall data in Korea. In addition, theoretical properties of the MA estimator are examined, including the asymptotic variance with random weights. A surrogate model of MA estimation is also developed and applied for further analysis. Finally, a Bayesian model averaging approach is considered to reduce the estimation bias occurring in the MA methods.

翻译：准确估计超出最大观测值的高分位数对于风险评估和制定有效适应策略以防止更大灾害至关重要。广义极值分布被广泛用于此目的，其中L-矩估计（LME）和最大似然估计（MLE）是主要方法。然而，当样本量较小且上端点无界（或等效地，外推过程中存在较大不确定性）时，高分位数估计变得极具挑战性。本研究引入了一种采用模型平均（MA）技术的改进方法。所提出的方法结合MLE和LME来构建候选子模型并有效分配权重。通过蒙特卡洛模拟及对韩国最大日降雨量数据的应用，评估了该方法的性能。此外，本文还检验了MA估计量的理论性质，包括具有随机权重的渐近方差。同时开发并应用了MA估计的代理模型以进行深入分析。最后，考虑采用贝叶斯模型平均方法来减少MA方法中出现的估计偏差。