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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


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.


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Jürgen Angst. Guillaume Poly. "A weak Cramér condition and application to Edgeworth expansions." Electron. J. Probab. 22 1 - 24, 2017.


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

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

Keywords: Cramér condition , Edgeworth expansion , small ball estimate

Vol.22 • 2017
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