極端污染事件通常呈現兩項關鍵特徵：局部最大值的強度與高門檻逾越的頻率。在極值理論中，廣義極值分布(Generalized Extreme Value; GEV)與廣義帕累托分布(Generalized Pareto Distribution; GPD)常用於描述此類現象。然而，存在顯著空間異質性時，單一模型往往難以同時兼顧這兩種特徵。為克服此限制，本研究提出一套以概似為基礎的模型平均架構，透過資料驅動的加權機制整合 GEV 與 GPD 模型。在廣義可加性位置、尺度與形狀模型架構下，我們將分布的參數建構為具空間平滑效果的線性預測式，並以懲罰式概似結合懲罰式迭代加權最小平方法進行估計；平滑參數則透過限制式最大概似法自動選取。進一步地，本研究建構一個以分位數為基礎的模型平均預測器，在相同分位數下對兩個模型的累積分布函數進行加權，並利用最大概似法由資料估計最佳權重。我們亦建立所提出方法的理論性質，證明該概似權重估計量具有一致性，且所得預測器在均方預測誤差準則下具備漸近最佳性。模擬結果顯示，相較於單一模型與固定權重方法，所提出的加權機制能有效提升預測表現，並可自適應地反映不同空間位置的尾端行為。最後，本研究將方法應用於臺灣 2019 至 2024 年每日PM2.5濃度資料，成功估計全臺空間變動之 GEV/GPD 的參數曲面，並進行高分位數預測，顯示本方法在極端污染分析上的實務應用價值。;Extreme pollution events typically exhibit two key characteristics: the magnitude of local maxima and the frequency of high-threshold exceedances. The generalized extreme value (GEV) and generalized Pareto distributions (GPD) are widely used in extreme value theory to characterize these behaviors. However， either model alone is often insufficient to simultaneously capture both features， particularly in the presence of substantial spatial heterogeneity. To address this limitation， we propose a flexible and spatially adaptive model averaging framework that integrates GEV and GPD models through a likelihood-based weighting scheme. Within the generalized additive models for location， scale， and shape (GAMLSS) framework， the distributional parameters are modeled as spatially smoothed linear predictors and estimated via penalized likelihood using penalized iteratively reweighted least squares (P-IRLS)， with smoothing parameters selected by restricted maximum likelihood (REML). A quantile-based model-averaged predictor is constructed by combining the cumulative distribution functions of the two extreme-value models at a common quantile through a data-driven weight， which is estimated via maximum likelihood. We establish theoretical properties of the proposed method， showing that the likelihood-based weight estimator is consistent and that the resulting predictor achieves asymptotic optimality under the mean squared prediction error criterion. Simulation studies demonstrate that the proposed weighting scheme improves predictive performance compared to single-model approaches and fixed-weight combinations， while adapting effectively to heterogeneous tail behaviors. Finally， an application to daily PM2.5 concentrations in Taiwan from 2019 to 2024 illustrates the practical utility of the proposed framework， including the estimation of spatially varying GEV/GPD parameter surfaces and accurate high-quantile prediction.
