Isaac Scientific Publishing

Journal of Advanced Statistics

Improved Estimator of Measure for Marginal Homogeneity using Marginal Odds in Square Contingency Tables

Download PDF (360.1 KB) PP. 71 - 77 Pub. Date: June 13, 2017

DOI: 10.22606/jas.2017.22001

Author(s)

  • Kiyotaka Iki*
    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan
  • Sadao Tomizawa

    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan

Abstract

For square contingency tables, Iki, Tahata and Tomizawa (2011) considered the measure to represent the degree of departure from the marginal homogeneity model. Using the first-order term in the Taylor series expansion, the estimated measure with the cell probabilities replaced by the corresponding sample proportions is an approximately unbiased estimator when the sample size is large. The present paper proposes the improved approximate unbiased estimator of the measure which is obtained by using the second-order term in the Taylor series expansion. Also, it shows that the improved estimator approaches to the true measure faster than the original estimator as the sample size becomes larger by the simulation studies.

Keywords

Estimation, marginal homogeneity, marginal odds, square contingency table, taylor series expansion, unbiased estimator.

References

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