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This paper proposes homological analysis of statistical dependency graph. If a dependency graph model satisfy the condition of a chain complex, homological algebra can be applied. Especially, the degree of freedom can be viewed as a dual space of an original complex. The calculation of homological and cohomological sequences is illustrated.
This paper proposes homological analysis of statistical dependency graph. If a dependency graph model satisfy the condition of a chain complex, homological algebra can be applied. Especially, the degree of freedom can be viewed as a dual space of an original complex.
This paper proposes homological analysis of statistical dependency graph. If a dependency graph model satisfy the condition of a chain complex, homological algebra can be applied. Especially, the degree of freedom can be viewed as a dual space of an original complex.
This paper focuses on the degree of freedom and number of subdetermiants in a pearson residual in a multiway contingency table. 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, the number of subderminants in a residual is equal to...
This paper focuses on geometrical intepretation of pearson residual, which measures the degree of statistical depedendence of a given cell. An information granule of statistical independence at a given cell is represented as a square whose origin is the given cell. Interestingly, the degree of freedom of each cell is equal to the number of squares at the cell, which can be extended to mult-way contingency...
This paper gives further investigation on correlation between pearson residuals and degree of freedom in a contingency table. An interesting formula is obtained, where an independent variable in a contingency table will be a fundamental granule of degree of freedom. The structure of formula is also closely related with combinatorial natures of given variables.
This paper focuses on residual analysis of statistical independence of multiple variables from the viewpoint of linear algebra. 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.
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