Dependence and Uncertainty: Information Measures using Tsallis Entropy
依赖与不确定性：基于 Tsallis 熵的信息度量AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要核心是一般依赖信息度量，金融时间序列仅作示例，未明确研究定价、波动率、风险或收益预测。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
依赖与不确定性：基于 Tsallis 熵的信息度量
- 研究问题
- 当 copula 密度不存在时，如何仍然度量多变量依赖结构与不确定性，并构造互信息指标和相互独立性检验？
- 方法与思路
- 作者将累计 copula 信息框架扩展至 Tsallis 熵，推导性质与界，构造非参数度量、累计互信息及相互独立性检验。
- 材料陈述的贡献
- 摘要称提出累计 copula 熵及相关不准确度、散度和互信息度量，并通过动力系统例子与双变量金融时间序列展示用途。
- 阅读关注点
- 应核对各累计度量的定义、对奇异 copula 的适用性、熵参数作用，以及非参数估计和独立性检验的统计校准。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核验。摘要未提供检验条件或性能数值，金融例子不足以验证指标的经济含义。
原文摘要
In multivariate analysis, uncertainty arises from two sources: the marginal distributions of the variables and their dependence structure. Quantifying the dependence structure is crucial, as it provides valuable insights into the relationships among components of a random vector. Copula functions effectively capture this dependence structure independent of marginals, making copula-based information measures highly significant. However, existing copula-based information measures, such as entropy, divergence, and mutual information, rely on copula densities, which may not exist in many scenarios, limiting their applicability. Recently, to address this issue, Arshad et al. (2024) introduced cumulative copula-based measures using Shannon entropy. In this paper, we extend this framework by using Tsallis entropy, a non-additive entropy that provides greater flexibility for quantifying uncertainties. We propose cumulative copula Tsallis entropy, derive its properties and bounds, and illustrate its utility through examples. We further develop a non-parametric version of the measure and validate it using coupled periodic and chaotic maps. Additionally, we extend Kerridge's inaccuracy measure and Kullback-Leibler (KL) divergence to the cumulative copula framework. Using the relationship between KL divergence and mutual information, we propose a new cumulative mutual information (CMI) measure, which outperform the limitations of density-based mutual information. Furthermore, we introduce a test procedure for testing the mutual independence among random variables using CMI measure. Finally, we illustrate the potential of the proposed CMI measure as an economic indicator through real bivariate financial time series data.