On metric spaces of subcopulas
© 2020 In this work, we show that two distance functions independently defined on the space of subcopulas are topological equivalent. In this process, we also defined another distance function equivalent to the first two distances. Moreover, all metric spaces of subcopulas with fixed domain under th...
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th-cmuir.6653943832-704422020-10-14T08:40:13Z On metric spaces of subcopulas Santi Tasena Computer Science Mathematics © 2020 In this work, we show that two distance functions independently defined on the space of subcopulas are topological equivalent. In this process, we also defined another distance function equivalent to the first two distances. Moreover, all metric spaces of subcopulas with fixed domain under the supremum distance are metric subspaces under this new distance function. We also prove that the Sklar correspondence can be viewed as a Lipschitz map under these metrics. Thus, the rate of convergence of empirical subcopulas can be computed directly from the rate of convergence of empirical distributions. The same holds for other statistics results. 2020-10-14T08:30:57Z 2020-10-14T08:30:57Z 2020-01-01 Journal 01650114 2-s2.0-85082683939 10.1016/j.fss.2020.03.021 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082683939&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70442 |
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Computer Science Mathematics Santi Tasena On metric spaces of subcopulas |
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© 2020 In this work, we show that two distance functions independently defined on the space of subcopulas are topological equivalent. In this process, we also defined another distance function equivalent to the first two distances. Moreover, all metric spaces of subcopulas with fixed domain under the supremum distance are metric subspaces under this new distance function. We also prove that the Sklar correspondence can be viewed as a Lipschitz map under these metrics. Thus, the rate of convergence of empirical subcopulas can be computed directly from the rate of convergence of empirical distributions. The same holds for other statistics results. |
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Journal |
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Santi Tasena |
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Santi Tasena |
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Santi Tasena |
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On metric spaces of subcopulas |
| title_short |
On metric spaces of subcopulas |
| title_full |
On metric spaces of subcopulas |
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On metric spaces of subcopulas |
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On metric spaces of subcopulas |
| title_sort |
on metric spaces of subcopulas |
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2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082683939&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70442 |
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