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Local Pinsker inequalities via Stein’s discrete density approach

par Ley, Christophe ;Swan, Yvik
Référence IEEE Transactions on Information Theory, 59, page (5584-5591)
Publication Publié, 2013

Article révisé par les pairs

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Résumé :

Pinsker's inequality states that the relative entropy d_{KL}(X;Y)between two random variables X and Y dominates the square of the totalvariation distance d_{TV}(X; Y) between X and Y. In this paper we intro-duce generalized Fisher information distances J (X;Y) between discretedistributions X and Y and prove that these also dominate the square ofthe total variation distance. To this end we introduce a general discreteStein operator for which we prove a useful covariance identity. We illustrateour approach with several examples. Whenever competitor inequalities areavailable in the literature, the constants in ours are at least as good, and,in several cases, better.