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- Christophe Ley, Yvik Swan
- 2012

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in… (More)

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de Bruijn's identity of information theory. When applied to sequences of functionals of a general Gaussian field, our… (More)

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… (More)

—We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced in [19] and also provide a new proof of a central identity first discovered in [7]. We derive a representation for the… (More)

In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredients, we derive an explicit and simple formula for the derivative of the input-output mutual information of this non-linear channel with respect to the channel quality parameter.… (More)

Let X = {X n } n≥1 and Y = {Y n } n≥1 be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums These rates are seen to hold for the convergence of a number of important statistics, such as for instance Student's t-statistic or the empirical correlation coefficient.

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