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

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.

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

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1068.60008
MathSciNet: MR2123202
Digital Object Identifier: 10.1214/009117904000000766

Subjects:
Primary: 60A10
Secondary: 52A20 , 60B10 , 62B10

Keywords: Accessible face , convex core , convex support , exponential family , Extension‎ , information divergence , variation distance , weak convergence

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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