Electronic Communications in Probability

Asymptotic constants for minimal distance in the central limit theorem

Emmanuel Rio

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Abstract

In this paper, we generalize the asymptotic result of Esseen (1958) concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances of order $r$ for $r \in ]1,2]$.

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 9, 96-103.

Dates
Accepted: 22 December 2011
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465261965

Digital Object Identifier
doi:10.1214/ECP.v16-1609

Mathematical Reviews number (MathSciNet)
MR2772388

Zentralblatt MATH identifier
1225.60047

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Minimal metric Wasserstein distance Cornish-Fisher expansion of first order Esseen's mean central limit theorem Global central limit theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Rio, Emmanuel. Asymptotic constants for minimal distance in the central limit theorem. Electron. Commun. Probab. 16 (2011), paper no. 9, 96--103. doi:10.1214/ECP.v16-1609. https://projecteuclid.org/euclid.ecp/1465261965


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References

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