Combinatorics in Pearson residuals

Authors:
Shusaku Tsumoto;Shoji Hirano
Affiliations:
Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho Izumo 693-8501, Japan;Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho Izumo 693-8501, Japan
Venue:
International Journal of Knowledge Engineering and Soft Data Paradigms
Year:
2013

Citing 5
Cited 0

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Abstract

This paper focuses on residual analysis of statistical independence of multiple variables from the viewpoint of linear algebra and combinatorics. The results show that multidimensional residuals are represented as linear sum of determinants of 2 × 2 submatrices, which can be viewed as information granules measuring the degree of statistical dependence. Furthermore, all the elements of information granules have combinatorial characteristics of index sets.