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ArticleOriginal scientific text

Title

Information-type divergence when the likelihood ratios are bounded

Authors 1

Affiliations

  1. Department of Mathematics and Statistics, University of Maryland at Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250, U.S.A.

Abstract

The so-called ϕ-divergence is an important characteristic describing "dissimilarity" of two probability distributions. Many traditional measures of separation used in mathematical statistics and information theory, some of which are mentioned in the note, correspond to particular choices of this divergence. An upper bound on a ϕ-divergence between two probability distributions is derived when the likelihood ratio is bounded. The usefulness of this sharp bound is illustrated by several examples of familiar ϕ-divergences. An extension of this inequality to ϕ-divergences between a finite number of probability distributions with pairwise bounded likelihood ratios is also given.

Keywords

ENG
information measures, multiple decisions, convexity, likelihood ratio

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Applicationes Mathematicae
1996-1997/24/4
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Pages:
415-423
Main language of publication
English
Received
1996-09-16
Accepted
1996-12-10
Published
1997
Exact and natural sciences