Optical local Gaussian approximation of an exponential family
Summary Under certain regularity conditions products En of an experiment E can be locally approximated by homoschedastic Gaussian experiments Gn. Gn can be defined such that the square roots of the densities have nearly the same structure with respect to the L2-geometry as in En. The main result of...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1987
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| In: |
Probability theory and related fields
Year: 1987, Volume: 76, Issue: 1, Pages: 103-119 |
| ISSN: | 1432-2064 |
| DOI: | 10.1007/BF00390278 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/BF00390278 Verlag, Volltext: https://link.springer.com/article/10.1007/BF00390278 Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2FBF00390278.pdf 
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| Author Notes: | Enno Mammen |
| Summary: | Summary Under certain regularity conditions products En of an experiment E can be locally approximated by homoschedastic Gaussian experiments Gn. Gn can be defined such that the square roots of the densities have nearly the same structure with respect to the L2-geometry as in En. The main result of this paper is that this choice of Gn is asymptotically optimal in the sense of minimizing the deficiency distance between En and G if E is a one-dimensional exponential family. |
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| Item Description: | Gesehen am 01.03.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1432-2064 |
| DOI: | 10.1007/BF00390278 |