Local Pinsker inequalities via Stein's discrete density approach

2012/11/15 by Christophe Ley, Ley, Christophe, Yvik Swan +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Inequalities and Applications #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1211.3668

openalex publication_date 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Pinsker's inequality states that the relative entropy d_KL(X, Y) between two random variables X and Y dominates the square of the total variation distance d_TV(X,Y) between X and Y. In this paper we introduce generalized Fisher information distances J(X, Y) between discrete distributions X and Y and prove that these also dominate the square of the total variation distance. To this end we introduce a general discrete Stein operator for which we prove a useful covariance identity. We illustrate our approach with several examples. Whenever competitor inequalities are available in the literature, the constants in ours are at least as good, and, in several cases, better.

Citations

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