An information-theoretic approach to statistical dependence: Copula information
An information-theoretic approach to statistical dependence: Copula information
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DOI：
10.1209/0295-5075/88/68003
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发表时间：
2009-12-01
期刊：
影响因子：
1.8
通讯作者：
Vicente, R.
中科院分区：
文献类型：
--
作者：
Calsaverini, R. S.;Vicente, R.
我们讨论了信息和Copula理论之间的连接，表明Copula可以用来分解成边际和依赖成分的多元分布的信息内容，后者量化的互信息。我们将信息过剩定义为偏离最大熵分布的度量。还讨论了边际不变相关性测度的概念，并用于表明经验线性相关性低估了非高斯边际情况下实际相关性的幅度。互信息的Copula的渐近经验对数似然提供了一个上限。提供了一个解析表达式的信息过剩的T-copula，允许简单的模型识别在这个家庭。我们用一个财务数据集来说明这个框架。版权所有（C）EPLA，2009
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009