论文标题
所有用于估计极值指数的块最大值方法
All Block Maxima method for estimating the extreme value index
论文作者
论文摘要
极值分析中的块最大值（BM）方法拟合了块最大值的样本与广义极值（GEV）分布。我们考虑从样本中的所有潜在块，这导致了所有块最大值（ABM）估计器。与基于BM方法的现有估计器不同，ABM估计器是置换不变的。我们显示了ABM估计量的渐近行为，ABM估计量的渐近行为是使用BM方法在所有估计器中的渐近方差最低。模拟研究证明了我们的渐近理论是合理的。建立ABM估计量渐近理论的关键步骤是基于具有权重的高阶统计数据来获得尾巴经验过程的渐近扩展。
The block maxima (BM) approach in extreme value analysis fits a sample of block maxima to the Generalized Extreme Value (GEV) distribution. We consider all potential blocks from a sample, which leads to the All Block Maxima (ABM) estimator. Different from existing estimators based on the BM approach, the ABM estimator is permutation invariant. We show the asymptotic behavior of the ABM estimator, which has the lowest asymptotic variance among all estimators using the BM approach. Simulation studies justify our asymptotic theories. A key step in establishing the asymptotic theory for the ABM estimator is to obtain asymptotic expansions for the tail empirical process based on higher order statistics with weights.
