Multivariate Information Measures: A Copula-based Approach
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909279655559168 |
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| author | Arshad, Mohd. Zachariah, Swaroop Georgy Pathak, Ashok Kumar |
| author_facet | Arshad, Mohd. Zachariah, Swaroop Georgy Pathak, Ashok Kumar |
| contents | Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the uncertainty inherent in these dependencies. This paper introduces a multivariate variant of the cumulative copula entropy and explores its various properties, including bounds, stochastic orders, and convergence-related results. Additionally, we define a cumulative copula information generating function and derive it for several well-known families of multivariate copulas. A fractional generalization of the multivariate cumulative copula entropy is also introduced and examined. We present a non-parametric estimator of the cumulative copula entropy using empirical beta copula. Furthermore, we propose a new distance measure between two copulas based on the Kullback-Leibler divergence and discuss a goodness-of-fit test based on this measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivariate Information Measures: A Copula-based Approach Arshad, Mohd. Zachariah, Swaroop Georgy Pathak, Ashok Kumar Methodology Information Theory 62B10, 62H05, 94A17 Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the uncertainty inherent in these dependencies. This paper introduces a multivariate variant of the cumulative copula entropy and explores its various properties, including bounds, stochastic orders, and convergence-related results. Additionally, we define a cumulative copula information generating function and derive it for several well-known families of multivariate copulas. A fractional generalization of the multivariate cumulative copula entropy is also introduced and examined. We present a non-parametric estimator of the cumulative copula entropy using empirical beta copula. Furthermore, we propose a new distance measure between two copulas based on the Kullback-Leibler divergence and discuss a goodness-of-fit test based on this measure. |
| title | Multivariate Information Measures: A Copula-based Approach |
| topic | Methodology Information Theory 62B10, 62H05, 94A17 |
| url | https://arxiv.org/abs/2408.02028 |