论文标题
双变量数据的身体和尾巴的联合建模
Joint modelling of the body and tail of bivariate data
论文作者
论文摘要
在极端数据和非极端数据都令人感兴趣的情况下，准确地对整个数据进行建模非常重要。在单变量框架中，对分布的大块和尾部进行建模之前已经进行了广泛的研究。但是，当关注多个变量时，文献中专门旨在正确捕获两个区域的模型在文献中很少。提出了一个在整个数据支持范围内混合两个具有不同特征的Copulas的依赖模型。一个副本是针对散装量身定制的，另一个是针对尾巴的，其动态加权功能在它们之间顺利过渡。对尾部依赖性进行数值研究，并使用模拟来确认混合模型足够灵活以捕获各种结构。该模型用于研究英国两个地点的温度和臭氧浓度之间的依赖性，并与单个副柱拟合进行了比较。所提出的模型为数据提供了更好，更灵活的，也可以捕获复杂的依赖性结构。
In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before. However, when more than one variable is of concern, models that aim specifically at capturing both regions correctly are scarce in the literature. A dependence model that blends two copulas with different characteristics over the whole range of the data support is proposed. One copula is tailored to the bulk and the other to the tail, with a dynamic weighting function employed to transition smoothly between them. Tail dependence properties are investigated numerically and simulation is used to confirm that the blended model is sufficiently flexible to capture a wide variety of structures. The model is applied to study the dependence between temperature and ozone concentration at two sites in the UK and compared with a single copula fit. The proposed model provides a better, more flexible, fit to the data, and is also capable of capturing complex dependence structures.
