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2017 A weak Cramér condition and application to Edgeworth expansions
Jürgen Angst, Guillaume Poly
Electron. J. Probab. 22: 1-24 (2017). DOI: 10.1214/17-EJP77

Abstract

We introduce a new, weak Cramér condition on the characteristic function of a random vector which does not only hold for all continuous distributions but also for discrete (non-lattice) ones in a generic sense. We then prove that the normalized sum of independent random vectors satisfying this new condition automatically verifies some small ball estimates and admits a valid Edgeworth expansion for the Kolmogorov metric. The latter results therefore extend the well known theory of Edgeworth expansion under the standard Cramér condition, to distributions that are purely discrete.

Citation

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Jürgen Angst. Guillaume Poly. "A weak Cramér condition and application to Edgeworth expansions." Electron. J. Probab. 22 1 - 24, 2017. https://doi.org/10.1214/17-EJP77

Information

Received: 18 January 2016; Accepted: 15 June 2017; Published: 2017
First available in Project Euclid: 20 July 2017

zbMATH: 1380.60027
MathSciNet: MR3683368
Digital Object Identifier: 10.1214/17-EJP77

Subjects:
Primary: 60E10, 60G50, 62E17, 62E20

JOURNAL ARTICLE
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