Open Access
November 2016 Asymptotic development for the CLT in total variation distance
Vlad Bally, Lucia Caramellino
Bernoulli 22(4): 2442-2485 (November 2016). DOI: 10.3150/15-BEJ734


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 22 (4) 2442 - 2485, November 2016.


Received: 1 July 2014; Revised: 1 February 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1346.60016
MathSciNet: MR3498034
Digital Object Identifier: 10.3150/15-BEJ734

Keywords: abstract Malliavin calculus , integration by parts , regularizing functions , total variation distance

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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