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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 3, Pages 563-569

An edgeworth expansion for a sum of M-Dependent random variables

Faculty of Management Sciences, The Ohio State University, Columbus 43210, Ohio, USA

Received 20 February 1985

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given a sequence X1,X2,,Xn of m-dependent random variables with moments of order 3+α (0<α1), we give an Edgeworth expansion of the distribution of Sσ1(S=X1+X2++Xn, σ2=ES2) under the assumption that E[exp(it Sσ1)] is small away from the origin. The result is of the best possible order.