Parametrized measure models

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00486135" target="_blank" >RIV/67985840:_____/18:00486135 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3150/16-BEJ910" target="_blank" >http://dx.doi.org/10.3150/16-BEJ910</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3150/16-BEJ910" target="_blank" >10.3150/16-BEJ910</a>

Result language
angličtina
Original language name
Parametrized measure models
Original language description
We develop a new and general notion of parametric measure models and statistical models on an arbitrary sample space Omega which does not assume that all measures of the model have the same null sets. This is given by a differentiable map from the parameter manifold M into the set of finite measures or probability measures on Omega, respectively, which is differentiable when regarded as a map into the Banach space of all signed measures on Omega. Furthermore, we also give a rigorous definition of roots of measures and give a natural characterization of the Fisher metric and the Amari-Chentsov tensor as the pullback of tensors defined on the space of roots of measures. We show that many features such as the preservation of this tensor under sufficient statistics and the monotonicity formula hold even in this very general set-up.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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