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December, 1990 Lancaster Interactions Revisited
Bernd Streitberg
Ann. Statist. 18(4): 1878-1885 (December, 1990). DOI: 10.1214/aos/1176347885

Abstract

Additive interactions of $n$-dimensional random vectors $X$, as defined by Lancaster, do not necessarily vanish for $n \geq 4$ if $X$ consists of two mutually independent subvectors. This defect is corrected and an explicit formula is derived which coincides with Lancaster's definition for $n < 4$. The new definition leads also to a corrected Bahadur expansion and has certain connections to cumulants. The main technical tool is a characterization theorem for the Moebius function on arbitrary finite lattices.

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Bernd Streitberg. "Lancaster Interactions Revisited." Ann. Statist. 18 (4) 1878 - 1885, December, 1990. https://doi.org/10.1214/aos/1176347885

Information

Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0713.62056
MathSciNet: MR1074442
Digital Object Identifier: 10.1214/aos/1176347885

Subjects:
Primary: 62E10
Secondary: 62E30

Keywords: Additive interactions , Bahadur expansions , Contingency tables , Cumulants , Moebius function , partition lattice

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 4 • December, 1990
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