Asymptotic development for the CLT in total variation distance

Vlad Bally 1, 2 Lucia Caramellino 3
2 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
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. Asymptotic development for the CLT in total variation distance. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2016, 22, pp.2442-2485. ⟨hal-01104866⟩

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