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.
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)