English

Closures of exponential families

Probability 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0503653,
  title  = {Closures of exponential families},
  author = {Imre Csiszar and Frantisek Matus},
  journal= {arXiv preprint arXiv:math/0503653},
  year   = {2007}
}

Comments

Published at http://dx.doi.org/10.1214/009117904000000766 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

R2 v1 2026-07-22T17:17:26.927Z