标题： 基于最大稳定过程和边际点过程的加利福尼亚州降水极端值的两步建模方法 显示英文标题

标题： A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes

摘要： 在建模空间极值时，经典的依赖结构推断方法假设块极大值来源于最大稳定过程。气象站提供的是每日记录而非仅仅块极大值。一些从业者更喜欢的点过程方法，由于使用了更多的历史数据，在单变量极值分析中表现出优势，但难以直接应用于空间设置。我们提出了一种两步法，结合复合似然函数，利用站点每日记录和块极大值。该方法将边缘参数估计和依赖参数估计分成了两个步骤。第一步使用点过程方法中的独立似然函数，基于每日记录来估计边缘参数。在已知边缘参数估计的情况下，第二步使用成对似然函数，基于块极大值来估计依赖参数。在模拟研究中发现，与仅使用块极大值的成对似然法相比，该两步法更为高效。该方法被用于研究厄尔尼诺-南方涛动（ENSO）对加利福尼亚极端降水的影响，基于55年间35个站点的最大冬季日降水量。使用站点特定的广义极值模型后，两步法检测到更多具有厄尔尼诺效应的站点，返回水平的置信区间更窄，并且联合定义事件的风险度量的置信区域更紧凑。 显示英文摘要

摘要： In modeling spatial extremes, the dependence structure is classically inferred by assuming that block maxima derive from max-stable processes. Weather stations provide daily records rather than just block maxima. The point process approach for univariate extreme value analysis, which uses more historical data and is preferred by some practitioners, does not adapt easily to the spatial setting. We propose a two-step approach with a composite likelihood that utilizes site-wise daily records in addition to block maxima. The procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal parameters with an independence likelihood from the point process approach using daily records. Given the marginal parameter estimates, the second step estimates the dependence parameters with a pairwise likelihood using block maxima. In a simulation study, the two-step approach was found to be more efficient than the pairwise likelihood approach using only block maxima. The method was applied to study the effect of El Ni\~{n}o-Southern Oscillation on extreme precipitation in California with maximum daily winter precipitation from 35 sites over 55 years. Using site-specific generalized extreme value models, the two-step approach led to more sites detected with the El Ni\~{n}o effect, narrower confidence intervals for return levels and tighter confidence regions for risk measures of jointly defined events.