TY - JOUR
T1 - On edgeworth expansions for dependency-neighborhoods chain structures and Stein's method
AU - Rinott, Yosef
AU - Rotar, Vladimir
PY - 2003/8
Y1 - 2003/8
N2 - Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary "length" for E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W, The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.
AB - Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary "length" for E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W, The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.
KW - Edgeworth expansion
KW - Local dependency
KW - Non-complete U-statistics
KW - Stein's method
UR - http://www.scopus.com/inward/record.url?scp=0042834085&partnerID=8YFLogxK
U2 - 10.1007/s00440-003-0271-5
DO - 10.1007/s00440-003-0271-5
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AN - SCOPUS:0042834085
SN - 0178-8051
VL - 126
SP - 528
EP - 570
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 4
ER -