Kouji Tahata, Hiroyuki Tanaka, Sadao Tomizawa
Department of Information Sciences
Faculty of Science and Technology
Tokyo University of Science
2641 Yamazaki, Noda City, Chiba, 278-8510, JAPAN

Abstract. For square contingency tables, Tomizawa [6], Tomizawa and Makii [7] and Tomizawa, Miyamoto and Ashihara [8] considered the measures to represent the degree of departure from the marginal homogeneity model.

Using the first-order term in the Taylor series expansion, the estimated measures with the cell probabilities replaced by the corresponding sample proportions are approximately unbiased estimators of the corresponding measures when the sample size is large.

This paper proposes the refined 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.

Received: October 30, 2013

AMS Subject Classification: 62H17

Key Words and Phrases: estimation, marginal homogeneity, square contingency table, Taylor series expansion, unbiased estimators

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