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Pinsker's inequality states that the relative entropy $d_{\mathrm{KL}}(X, Y)$ between two random variables $X$ and $Y$ dominates the square of the total variation distance $d_{\mathrm{TV}}(X,Y)$ between $X$ and $Y$.
A lower bound for discrimination information in terms of variation
S. Kullback · 1967
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On Fisher’s amount of information for location family
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A proof of the central limit theorem motivated by the Cramér-Rao inequality
L. D. Brown · 1982
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A. R. Barron · 1986
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Une mesure d’information caractérisant la loi de poisson
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Entropy production by block variable summation and central limit theorems
E. Carlen and A. Soffer · 1991
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Poisson approximation
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Entropy jumps in the presence of a spectral gap
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Stein’s method for birth and death chains
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Information theory and the central limit theorem
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An introduction to Stein’s method
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Elements of Information Theory
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The discrete Mohr and Noll inequality with applications to variance bounds
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Stein’s method and the rank distribution of random matrices over finite fields
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Stein’s method and the beta distribution
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Stein’s method for discrete gibbs measures
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Compound Poisson approximation via information functionals
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An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
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Normal approximation by Stein’s method
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