Asymptotic development for the CLT in total variation distance

Vlad Bally; Lucia Caramellino

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arXiv · 1407.0896

Asymptotic development for the CLT in total variation distance

Vlad Bally·Lucia Caramellino

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Abstract

The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely continuous component): we develop the error in powers of $n^{-1/2}$ and give an explicit formula for the approximating measure.

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Vlad Bally, Lucia Caramellino. 2016-04-11. Asymptotic development for the CLT in total variation distance. https://arxiv.org/abs/1407.0896

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