Closures of exponential families

Details Closures of exponential families Closures of exponential families

2005-03-29

arxiv.org/abs/math/0503653v1

Annals of Probability 2005, Vol. 33, No. 2, 582-600

Mathematics

Probability

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

Scientific paper

10.1214/009117904000000766

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.

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