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

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.

Keywords

• Edgeworth expansion
• m-dependent
• Berry-Esseen bound
• Central limit theorem.