# Information-type divergence when the likelihood ratios are bounded

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 4, page 415-423
- ISSN: 1233-7234

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topRukhin, Andrew. "Information-type divergence when the likelihood ratios are bounded." Applicationes Mathematicae 24.4 (1997): 415-423. <http://eudml.org/doc/219181>.

@article{Rukhin1997,

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.},

author = {Rukhin, Andrew},

journal = {Applicationes Mathematicae},

keywords = {information measures; multiple decisions; convexity; likelihood ratio},

language = {eng},

number = {4},

pages = {415-423},

title = {Information-type divergence when the likelihood ratios are bounded},

url = {http://eudml.org/doc/219181},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Rukhin, Andrew

TI - Information-type divergence when the likelihood ratios are bounded

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 4

SP - 415

EP - 423

AB - 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.

LA - eng

KW - information measures; multiple decisions; convexity; likelihood ratio

UR - http://eudml.org/doc/219181

ER -

## References

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