International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 563-569
doi:10.1155/S0161171285000618
An edgeworth expansion for a sum of M-Dependent random variables
Wan Soo Rhee
Faculty of Management Sciences, The Ohio State University, Columbus 43210, Ohio, USA
Abstract
Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1), we give an Edgeworth expansion of the distribution of Sσ−1(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.