Refinements of Pinsker's inequality

Refinements of Pinsker's inequality

Let V and D denote, respectively, total variation and divergence. We study lower bounds of D with V fixed. The theoretically best (i.e., largest) lower bound determines a function L=L(V), Vajda's (1970) tight lower bound. The main result is an exact parametrization of L. This leads to Taylor po...

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Veröffentlicht in:IEEE transactions on information theory 2003-06, Vol.49 (6), p.1491-1498
Hauptverfasser: Fedotov, A.A., Harremoes, P., Topsoe, F.
Format: Artikel
Sprache:eng
Schlagworte:
Additives
Councils
Divergence
Entropy
Followers
Inequalities
Information systems
Information technology
Information theory
Lower bounds
Mathematics
Parametrization
Polynomials
Random variables
Upper bound
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Beschreibung
Zusammenfassung:Let V and D denote, respectively, total variation and divergence. We study lower bounds of D with V fixed. The theoretically best (i.e., largest) lower bound determines a function L=L(V), Vajda's (1970) tight lower bound. The main result is an exact parametrization of L. This leads to Taylor polynomials which are lower bounds for L, and thereby to extensions of the classical Pinsker (1960) inequality which has numerous applications, cf. Pinsker and followers.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.811927