Fréchet Means in Infinite Dimensions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911728916234240 |
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| author | Jaffe, Adam Quinn |
| author_facet | Jaffe, Adam Quinn |
| contents | While there exists a well-developed asymptotic theory of Fréchet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in an "infinite-dimensional" metric space. Presently, we develop a general asymptotic theory of Fréchet means in some infinite-dimensional metric spaces, which allows us to recover, strengthen, and generalize most existing results; in particular, we develop novel asymptotic theory for Fréchet means in some infinite-dimensional metric spaces from statistical shape analysis. The core of the proof is a novel notion of weak convergence in general metric spaces for which the results can be proven via calculus of variations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fréchet Means in Infinite Dimensions Jaffe, Adam Quinn Probability Functional Analysis Metric Geometry 46T20, 49J52, 60F15, 62R20 While there exists a well-developed asymptotic theory of Fréchet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in an "infinite-dimensional" metric space. Presently, we develop a general asymptotic theory of Fréchet means in some infinite-dimensional metric spaces, which allows us to recover, strengthen, and generalize most existing results; in particular, we develop novel asymptotic theory for Fréchet means in some infinite-dimensional metric spaces from statistical shape analysis. The core of the proof is a novel notion of weak convergence in general metric spaces for which the results can be proven via calculus of variations. |
| title | Fréchet Means in Infinite Dimensions |
| topic | Probability Functional Analysis Metric Geometry 46T20, 49J52, 60F15, 62R20 |
| url | https://arxiv.org/abs/2410.17214 |