The uniqueness of the Fisher metric as information metric
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476158" target="_blank" >RIV/67985840:_____/17:00476158 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10463-016-0562-0" target="_blank" >http://dx.doi.org/10.1007/s10463-016-0562-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10463-016-0562-0" target="_blank" >10.1007/s10463-016-0562-0</a>
Alternative languages
Result language
angličtina
Original language name
The uniqueness of the Fisher metric as information metric
Original language description
We define a mixed topology on the fiber space (Formula presented.) over the space (Formula presented.) of all finite non-negative measures (Formula presented.) on a separable metric space (Formula presented.) provided with Borel (Formula presented.)-algebra. We define a notion of strong continuity of a covariant n-tensor field on (Formula presented.). Under the assumption of strong continuity of an information metric, we prove the uniqueness of the Fisher metric as information metric on statistical models associated with (Formula presented.). Our proof realizes a suggestion due to Amari and Nagaoka to derive the uniqueness of the Fisher metric from the special case proved by Chentsov by using a special kind of limiting procedure. The obtained result extends the monotonicity characterization of the Fisher metric on statistical models associated with finite sample spaces and complement the uniqueness theorem by Ay–Jost–Le–Schwachhöfer that characterizes the Fisher metric.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of the Institute of Statistical Mathematics
ISSN
0020-3157
e-ISSN
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Volume of the periodical
69
Issue of the periodical within the volume
4
Country of publishing house
JP - JAPAN
Number of pages
18
Pages from-to
879-896
UT code for WoS article
000405510700007
EID of the result in the Scopus database
2-s2.0-84968546909