Advances and Applications in Statistics
Volume 7, Issue 1, Pages 47 - 63
(April 2007)
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IMPROVED APPROXIMATE UNBIASED ESTIMATORS OF MEASURES OF ASYMMETRY FOR SQUARE CONTINGENCY TABLES
Sadao Tomizawa (Japan), Nobuko Miyamoto (Japan) and Noriaki Ohba (Japan)
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Abstract: For square contingency tables, Tomizawa [6], Tomizawa et al. [8] and Tomizawa et al. [7] considered the measures to represent the degree of departure from the symmetry model. Using the delta method, the estimated measures with the probabilities replaced by the sample proportions are approximately unbiased estimators of the corresponding measures when the sample size is large. This paper proposes the improved approximate unbiased estimators of the measures which are obtained by using the second-order term in the Taylor series expansion. The improved estimators approach to the true measures faster than the original estimators as the sample size becomes larger. These are shown by the simulation studies. |
Keywords and phrases: delta method, measure, square contingency table, symmetry, unbiased estimator. |
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