The Cramér-Rao inequality on singular statistical models

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00481328" target="_blank" >RIV/67985840:_____/17:00481328 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/978-3-319-68445-1_64" target="_blank" >http://dx.doi.org/10.1007/978-3-319-68445-1_64</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-68445-1_64" target="_blank" >10.1007/978-3-319-68445-1_64</a>

Result language

angličtina

Original language name

The Cramér-Rao inequality on singular statistical models

Original language description

We introduce the notions of essential tangent space and reduced Fisher metric and extend the classical Cramér-Rao inequality to $2$-integrable (possibly singular) statistical models for general $varphi$-estimators, where $varphi$ is a $V$-valued feature function and $V$ is a topological vector space. We show the existence of a $varphi$-efficient estimator on strictly singular statistical models associated with a finite sample space and on a class of infinite dimensional exponential models that have been discovered by Fukumizu. We conclude that our general Cramér-Rao inequality is optimal.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

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

Article name in the collection

Geometric Science of Information. GSI 2017

ISBN

978-3-319-68444-4

ISSN

0302-9743

e-ISSN

—

Number of pages

9

Pages from-to

552-560

Publisher name

Springer

Place of publication

Cham

Event location

Paris

Event date

Nov 7, 2017

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000440482500064