ESTIMATING THE EXTREME VALUE INDEX AND HIGH QUANTILES WITH EXPONENTIAL REGRESSION MODELS
ESTIMATING THE EXTREME VALUE INDEX AND HIGH QUANTILES WITH EXPONENTIAL REGRESSION MODELS
复制标题
用指数回归模型估计极值指数和高分位数
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Beirlant
中科院分区：
文献类型：
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作者：
Gunther Matthys;J. Beirlant
在本文中，我们提出了指数回归模型的间距，或有序超过一个给定的阈值，并在最大域的吸引力条件下，这种间距的对数比。从这些，我们得到的极值指数（EVI）和高分位数的估计，它共享许多有吸引力的性质的最大似然估计的峰值超过阈值的方法，但提供的额外的优点是普遍适用的，而不限制的值的EVI。此外，指数回归模型可以用二阶正则变差的参数来改进，这减少了所得估计量的偏差。改进后的模型还产生了有见地和实用的技术，以选择在估计经济脆弱性指数和高分位数的阈值。我们证明了新提出的估计器的渐近正态性，并在模拟研究中将其小样本行为与一些经典方法进行了比较。
In this paper we present exponential regression models for spacings, or ordered excesses over a given threshold, and for log-ratios of such spacings under maximum domain of attraction conditions. From these we derive estimators for the extreme value index (EVI) and for high quantiles, which share many attractive properties of the maximum likelihood estimators from the peaks-over-thresholds method, but offer the extra advantage of being generally applicable without re- striction on the value of the EVI. Further, the exponential regression models can be refined with parameters of second order regular variation, which reduces the bias of the resulting estimators. The refined models also give rise to insightful and practical techniques to select the threshold in the estimation of the EVI and of high quantiles. We demonstrate asymptotic normality of the newly proposed esti- mators and compare their small sample behaviour to some classical methods in a simulation study.