The Annals of Statistics

Lancaster Interactions Revisited

Bernd Streitberg

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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.

Article information

Source
Ann. Statist., Volume 18, Number 4 (1990), 1878-1885.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347885

Digital Object Identifier
doi:10.1214/aos/1176347885

Mathematical Reviews number (MathSciNet)
MR1074442

Zentralblatt MATH identifier
0713.62056

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62E30

Keywords
Additive interactions Bahadur expansions cumulants Moebius function partition lattice contingency tables

Citation

Streitberg, Bernd. Lancaster Interactions Revisited. Ann. Statist. 18 (1990), no. 4, 1878--1885. doi:10.1214/aos/1176347885. https://projecteuclid.org/euclid.aos/1176347885


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