The uniqueness of the Fisher metric as information metric

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The uniqueness of the Fisher metric as information metric

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The uniqueness of the Fisher metric as information metric

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of the Institute of Statistical Mathematics

ISSN

0020-3157

e-ISSN

—

Svazek periodika

69

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

18

Strana od-do

879-896

Kód UT WoS článku

000405510700007

EID výsledku v databázi Scopus

2-s2.0-84968546909