Affine Gateaux Differentials and the von Mises Statistical Calculus
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909673554182144 |
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| author | Cerreia-Vioglio, Simone Maccheroni, Fabio Marinacci, Massimo Montrucchio, Luigi Stanca, Lorenzo |
| author_facet | Cerreia-Vioglio, Simone Maccheroni, Fabio Marinacci, Massimo Montrucchio, Luigi Stanca, Lorenzo |
| contents | This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear functionals typically employed in standard Gateaux differentiability. This affine notion of differentiability naturally arises in certain applications and has been utilized by some authors in the statistics literature. We aim to offer a unified and comprehensive perspective on this concept. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine Gateaux Differentials and the von Mises Statistical Calculus Cerreia-Vioglio, Simone Maccheroni, Fabio Marinacci, Massimo Montrucchio, Luigi Stanca, Lorenzo Functional Analysis Optimization and Control 49J50, 49J52, 26E15, 26B25 This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear functionals typically employed in standard Gateaux differentiability. This affine notion of differentiability naturally arises in certain applications and has been utilized by some authors in the statistics literature. We aim to offer a unified and comprehensive perspective on this concept. |
| title | Affine Gateaux Differentials and the von Mises Statistical Calculus |
| topic | Functional Analysis Optimization and Control 49J50, 49J52, 26E15, 26B25 |
| url | https://arxiv.org/abs/2403.07827 |