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.
Citation
Imre Csiszár. František Matúš. "Closures of exponential families." Ann. Probab. 33 (2) 582 - 600, March 2005. https://doi.org/10.1214/009117904000000766
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