ϕ-divergences, sufficiency, Bayes sufficiency, and deficiency

Title:

ϕ-divergences, sufficiency, Bayes sufficiency, and deficiency

Creator:

Liese, Friedrich

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5f779b23-abb3-428a-95fe-1b4a8a0cc140
uuid:5f779b23-abb3-428a-95fe-1b4a8a0cc140

Subject:

divergences, sufficiency, Bayes sufficiency, and deficiency

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

\vspace{-1.6cm} The paper studies the relations between ϕ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam's deficiency. A new and considerably simplified approach is given to the spectral representation of ϕ-divergences already established in Österreicher and Feldman \cite{OestFeld} under restrictive conditions and in Liese and Vajda \cite{LiV06}, \cite{LiV08} in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary convex functions which are strictly convex at one point only. Bayes sufficiency is characterized with the help of a binary model that consists of the joint distribution and the product of the marginal distributions of the observation and the parameter, respectively. LeCam's deficiency is expressed in terms of ϕ-divergences where ϕ belongs to a class of convex functions whose curvature measures are finite and satisfy a normalization condition.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[690]-713

Source:

Kybernetika | 2012 Volume:48 | Number:4

Harvested from:

CDK

Metadata only:

false