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