The Annals of Statistics
- Ann. Statist.
- Volume 18, Number 4 (1990), 1878-1885.
Lancaster Interactions Revisited
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.
Ann. Statist., Volume 18, Number 4 (1990), 1878-1885.
First available in Project Euclid: 12 April 2007
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Streitberg, Bernd. Lancaster Interactions Revisited. Ann. Statist. 18 (1990), no. 4, 1878--1885. doi:10.1214/aos/1176347885. https://projecteuclid.org/euclid.aos/1176347885