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Teor. Veroyatnost. i Primenen., 2007, Volume 52, Issue 1, Pages 21–40 (Mi tvp2)  

On edgeworth expansions for dependency-neighborhoods chain structures with strong mixing characteristics

V. I. Rotar'ab

a Central Economics and Mathematics Institute, RAS
b San Diego State University

Abstract: Let $W$ be the sum of dependent random variables, and let $h(x)$ be a function. This paper modifies results of [Y. Rinott and V. I. Rotar, Probab. Theory Related Fields, 126 (2003), pp. 528–570] concerning Edgeworth expansions for $\mathbf E\{h(W)\}$ in the case of the so-called dependency-neighborhoods structures. The most typical example of such structures is mixing on graphs. The main improvement consists in the replacement of $\phi$-mixing dependency characteristics by those of strong (or $\alpha$-) mixing, which essentially widens the possibilities of applications. Another improvement concerns the smoothness conditions. We show how conditions on the smoothness of $h$ may be replaced by conditions on the smoothness of the distribution of $W$.

DOI: https://doi.org/10.4213/tvp2

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English version:
Theory of Probability and its Applications, 2008, 52:1, 108–124

Bibliographic databases:

Received: 11.06.2005

Citation: V. I. Rotar', “On edgeworth expansions for dependency-neighborhoods chain structures with strong mixing characteristics”, Teor. Veroyatnost. i Primenen., 52:1 (2007), 21–40; Theory Probab. Appl., 52:1 (2008), 108–124

Citation in format AMSBIB
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