Testing for a multivariate generalized Pareto distribution
Testing for a multivariate generalized Pareto distribution
复制标题
多元广义帕累托分布的检验
DOI：
10.1007/s10687-008-0067-1
复制
发表时间：
2009
期刊：
影响因子：
1.3
通讯作者：
René Michel
中科院分区：
文献类型：
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作者：
M. Falk;René Michel
Rootzén和Tajvidi（Bernoulli，12：917-930，2006）最近表明，在多变量设置中，仅通过多变量广义帕累托分布（GPD）也可以合理地对高阈值上的随机变量的方差进行建模（峰值超过阈值方法[POT]）。然而，选择适当的阈值是一个关键问题。本文的贡献是双重的：首先，我们开发了一个非渐近和精确的水平α检验的基础上的单样本t检验，检查是否多元数据实际上是由一个多元GPD。其次，利用这一过程推导出了基于t检验的多变量峰过阈值模型的阈值选择规则。水文数据集的应用说明了这种方法。
It has recently been shown by Rootzén and Tajvidi (Bernoulli, 12:917–930, 2006) that modelling exceedances of a random variable over a high threshold (peaks-over-threshold approach [POT]) can also in the multivariate setup be done rationally only by a multivariate generalized Pareto distribution (GPD). The selection of a proper threshold is, however, a crucial problem. The contribution of this paper is twofold: We develop first a non asymptotic and exact level-α test based on the single-sample t-test, which checks whether multivariate data are actually generated by a multivariate GPD. Secondly, this procedure is utilized for the derivation of a t-test based threshold selection rule in multivariate peaks-over-threshold models. The application to a hydrological data set illustrates this approach.