Closures of exponential families

I. Csiszár, František Matúš

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential family, introduced previously by the authors, and a new concept of accessible faces of a convex set. Two other closures related to the information divergence are also characterized.

Original languageEnglish
Pages (from-to)582-600
Number of pages19
JournalAnnals of Probability
Volume33
Issue number2
DOIs
Publication statusPublished - Mar 2005

Fingerprint

Exponential Family
Convex Sets
Closure
Regularity Conditions
Divergence
Face
Concepts
Exponential family
Regularity

Keywords

  • Accessible face
  • Convex core
  • Convex support
  • Exponential family
  • Extension
  • Information divergence
  • Variation distance
  • Weak convergence

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Closures of exponential families. / Csiszár, I.; Matúš, František.

In: Annals of Probability, Vol. 33, No. 2, 03.2005, p. 582-600.

Research output: Contribution to journalArticle

Csiszár, I. ; Matúš, František. / Closures of exponential families. In: Annals of Probability. 2005 ; Vol. 33, No. 2. pp. 582-600.
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