2 1 Ju n 20 02 Convergence of the Poincaré constant
نویسنده
چکیده
The Poincaré constant RY of a random variable Y relates the L2(Y )-norm of a function g and its derivative g′. Since RY −Var (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 RY 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.
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