Structural decompositions of multivariate distributions with applications in moment and cumulant

Authors:
Edward H. Ip;Yuchung J. Wang;Yeong-nan Yeh
Affiliations:
Department of Public Health Sciences, Wake Forest University School of Medicine, Medical Center Boulevard, 3rd Floor, MRI Building, Winston-Salem, NC;Department of Mathematical Sciences, Rutgers University;Institute of Mathematics, Academia Sinica, Taiwan
Venue:
Journal of Multivariate Analysis
Year:
2004

Citing 5
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Abstract

We provide lattice decompositions for multivariate distributions. The lattice decompositions reveal the structural relationship between the Lancaster/Bahadur model and the model of Streitberg (Ann. Statist. 18 (1990) 1878). For multivariate categorical data, the decompositions allows modeling strategy for marginal inference. The theory discussed in this paper illustrates the concept of reproducibility, which was discussed in Liang et al. (J. Roy. Statist. Soc. Ser. B 54 (1992) 3). For the purpose of delineating the relationship between the various types of decompositions of distributions, we develop a theory of polytypefication, the generality of which is exploited to prove results beyond interaction.