Central Limit Theorem for Rényi Divergence of Infinite Order

2024/02/03 by Bobkov, Sergey G., Götze, Friedrich
#60E #60F #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.02259

Abstract

For normalized sums Z_n of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities p_n of Z_n, this is a strengthened variant of the local limit theorem taking the form sup_x (p_n(x) - φ(x))/φ(x) → 0 as n → ∞.

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• Rényi Divergences in Central Limit Theorems: Old and New
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