Closures of exponential families

Closures of exponential families

Imre Csiszár and František Matúš

Source: Ann. Probab. Volume 33, Number 2 (2005), 582-600.

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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Primary Subjects: 60A10

Secondary Subjects: 60B10, 62B10, 52A20

Keywords: Accessible face; convex core; convex support; exponential family; extension; information divergence; variation distance; weak convergence

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1109868592
Digital Object Identifier: doi:10.1214/009117904000000766
Zentralblatt MATH identifier: 02164474
Mathematical Reviews number (MathSciNet): MR2123202

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