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.
https://hal-upec-upem.archives-ouvertes.fr/hal-01104866
Contributor : Vlad Bally
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Submitted on : Monday, January 19, 2015 - 1:34:58 PM
Last modification on : Friday, October 4, 2019 - 1:38:44 AM
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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⟩
