On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method |
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| Authors: | Yosef Rinott Vladimir Rotar |
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| Affiliation: | (1) Department of Mathematics, University of California, San Diego, USA;(2) Department of Statistics, Hebrew University, Israel;(3) Department of Mathematics, San Diego State University, San Diego, USA;(4) the Central Economics and Mathematics, Institute of Russian Academy of Sciences, Russia |
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| Abstract: | ![]()
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.Supported in part by NSF grant DMS-98-03623Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05 |
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| Keywords: | Edgeworth expansion Local dependency Stein's method Non-complete U-statistics |
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