How to measure multidimensional variation?
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917851831468032 |
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| author | Auricchio, Gennaro Giudici, Paolo Toscani, Giuseppe |
| author_facet | Auricchio, Gennaro Giudici, Paolo Toscani, Giuseppe |
| contents | The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional Gini index, which measures the inequality of a distribution in terms of the mean differences among its observations. In this paper, we connect these two notions of sparsity, and propose a multidimensional coefficient of variation based on a multidimensional Gini index. We demonstrate that the proposed coefficient possesses the properties of the univariate coefficient of variation. We also show its connection with the Voinov-Nikulin coefficient of variation, and compare it with the other multivariate coefficients available in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to measure multidimensional variation? Auricchio, Gennaro Giudici, Paolo Toscani, Giuseppe Statistics Theory 62H20, 62H99 The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional Gini index, which measures the inequality of a distribution in terms of the mean differences among its observations. In this paper, we connect these two notions of sparsity, and propose a multidimensional coefficient of variation based on a multidimensional Gini index. We demonstrate that the proposed coefficient possesses the properties of the univariate coefficient of variation. We also show its connection with the Voinov-Nikulin coefficient of variation, and compare it with the other multivariate coefficients available in the literature. |
| title | How to measure multidimensional variation? |
| topic | Statistics Theory 62H20, 62H99 |
| url | https://arxiv.org/abs/2411.19529 |