Convergence of the Poincare constant

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The Poincare constant R-Y of a random variable Y relates the L-2(Y)-norm of a function g and its derivative g'. Since R-Y - D(Y) is positive, with equality if and only if Y is normal; it can be seen as a distance from the normal distribution. In this paper we establish the best possible rate of convergence of this distance in the central limit theorem. Furthermore, we show that R-Y is finite for discrete mixtures of normals, allowing us to add rates to the proof of the central limit theorem in the sense of relative entropy.
Translated title of the contributionConvergence of the Poincare constant
Original languageEnglish
Pages (from-to)535 - 541
Number of pages7
JournalTheory of Probability and its Applications
Volume48 (3)
Publication statusPublished - 2003

Bibliographical note

Publisher: SIAM Publications


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