Exact Cumulant Calculations for Pearson X2 and Zelterman Statistics for r-Way Contingency Tables |
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Authors: | James E. Stafford |
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Affiliation: | Department of Statistical and Actuarial Sciences , University of Western Ontario , London , Ontario , N6A 5B7 , Canada |
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Abstract: | Abstract We present a computer algebra procedure that calculates exact cumulants for Pearson X 2 and Zelterman statistics for r-way contingency tables. The algorithm is an example of how an overwhelming algebraic problem can be solved neatly through computer implementation by emulating tactics that one uses by hand. For inference purposes the cumulants may be used to assess chi-square approximations or to improve this approximation via Edgeworth expansions. Edgeworth approximations are compared to the computerintensive techniques of Mehta and Patel that provide exact and arbitrarily close results. Comparisons to approximations that utilize the gamma distribution (Mielke and Berry) are also made. |
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Keywords: | Computer algebra Edgeworth expansion Expectation Mathematica Nested sums Partitions Symbolic computation |
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