Title :
Refinements of Pinsker´s inequality
Author :
Fedotov, Alexei A. ; Harremoës, Peter ; Topsøe, Flemming
Author_Institution :
Dept. of Inf. Technol., Inst. of Computational Technol., Novosibirsk, Russia
fDate :
6/1/2003 12:00:00 AM
Abstract :
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.
Keywords :
information theory; polynomials; probability; set theory; Pinsker´s inequality; Taylor polynomials; Vaida´s tight lower bound; convex set; divergence; exact parametrization; information diagram; information theory; lower bounds; probability measures; total variation; Additives; Councils; Entropy; Information technology; Information theory; Mathematics; Notice of Violation; Polynomials; Random variables; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2003.811927
