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