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December 2021 Improved approximate unbiased estimators of the measure of departure from partial symmetry for square contingency tables
Tomoyuki Nakagawa, Ryoma Namba, Kiyotaka Iki, Sadao Tomizawa
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SUT J. Math. 57(2): 167-183 (December 2021). DOI: 10.55937/sut/1641859470

Abstract

For square contingency tables, the measure to represent the degree of departure from the partial symmetry model was proposed. It is necessary to estimate the measure because it is constructed of unknown parameters. Although many studies consider using the plug-in estimator to estimate the measure, the bias of the plug-in estimator is large when the sample size is not so large. In this study, we consider to estimate the measure when the sample size is not so large. This paper presents the improved approximate unbiased estimators of the measure which are obtained using the second-order term in Taylor series expansion. Some simulation studies show the performances of proposed estimators for finite sample cases.

Funding Statement

This work was supported by JSPS Grant-in-Aid for Scientific Research (C) Number JP20K03756, JSPS Grant-in-Aid for Scientific Research (C) Number JP18K03425 and JSPS Grant-in-Aid for Early-Career Scientists JP19K14600.

Acknowledgments

The authors would like to thank the referee and the editor for many comments and suggestions.

Citation

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Tomoyuki Nakagawa. Ryoma Namba. Kiyotaka Iki. Sadao Tomizawa. "Improved approximate unbiased estimators of the measure of departure from partial symmetry for square contingency tables." SUT J. Math. 57 (2) 167 - 183, December 2021. https://doi.org/10.55937/sut/1641859470

Information

Received: 11 May 2021; Published: December 2021
First available in Project Euclid: 21 April 2022

Digital Object Identifier: 10.55937/sut/1641859470

Subjects:
Primary: 62F12 , 62H17

Keywords: measure , partial symmetry , square contingency table , symmetry , unbiased estimator

Rights: Copyright © 2021 Tokyo University of Science

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Vol.57 • No. 2 • December 2021
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