块极大值图上极值的倾斜最大Lq-李克龙估计
Tilting maximum Lq-Likelihood estimation for extreme values drawing on block maxima
摘要：
在极值上应用主流最大似然推断的最常见的预期困难之一是阐明了极端观测的稀缺性，使极值定理在一系列最大值上成立。本文介绍了一种新的变形的Lq-似然方法，通过其与一个特殊的变形对数，保持自对偶性质的标准对数的联系。由于关注的是由每个子采样块内的那些最大值组成的相对较小的样本（通过将样本分割成相等长度的块），因此最大Lq估计将有利于减少与方差相关的不确定性，从而使偏差不受挑战。一项全面的模拟研究表明，采用更复杂的最大似然处理方法可改善对极端特征的估计，对收益水平估计有重大影响，而收益水平估计是许多容易发生极端灾害，如地震、洪水或流行病的业务环境的风险评估的一个关键组成部分。我们提供了一个说明性的例子，如何提出倾斜的Lq-似然可以改善极端事件的推断，通过借鉴公共卫生数据。
英文摘要：
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of maxima. This paper introduces a new variant of the Lq-likelihood method through its linkage with a particular deformed logarithm which preserves the self-dual property of the standard logarithm. Since the focus is on relatively small samples consisting of those maximum values within each sub-sampled block (by splitting the sample into blocks of equal length), the maximum Lq estimation will favour reducing uncertainty associated with the variance leaving the bias unchallenged. A comprehensive simulation study demonstrates that the introduction of a more sophisticated treatment of maximum likelihood improves the estimation of extreme characteristics, with significant implications for return-level estimation which is a crucial component in risk assessment for many operational settings prone to extreme hazards, such as earthquakes, floods or epidemics. We provide an illustrative example of how the proposed tilting of Lq-likelihood can improve inference on extreme events by drawing on public health data.
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