An extremal property of the normal distribution, with a discrete analog

Publication date: Available online 25 September 2018Source: Statistics & Probability LettersAuthor(s): Erwan Hillion, Oliver Johnson, Adrien SaumardAbstractWe give a new proof, using only the Brascamp–Lieb inequality, of the fact that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matrix. We unify the continuous and discrete settings by also giving a similar characterization of the Poisson measure in the discrete case, using “Chebyshev’s other inequality”. We briefly discuss how these results relate to Stein and Stein–Chen methods for Gaussian and Poisson approximation, and to the Bakry–Émery calculus.

Source: Statistics and Probability Letters - October 4, 2018 Category: Statistics Source Type: research