An index for measuring degree of departure from symmetry for ordinal square contingency tables

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Shuji Ando, Tomotaka Momozaki, Yuta Masusaki, Sadao Tomizawa
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引用次数: 0

Abstract

For the analysis of square contingency tables with the same row and column ordinal classifications, this study proposes an index for measuring the degree of departure from the symmetry model using new cumulative probabilities. The proposed index is constructed based on the Cressie and Read’s power divergence, or the weighted average of the Patil and Taillie’s diversity index. This study derives a plug-in estimator of the proposed index and an approximate confidence interval for the proposed index. The estimator of the proposed index is expected to reduce the bias more than the estimator of the existing index, even when the sample size is not large. The proposed index is identical to the existing index under the conditional symmetry model. Therefore, assuming the probability structure in which the conditional symmetry model holds, the performances of plug-in estimators of the proposed and existing indexes can be simply compared. Through numerical examples and real data analysis, the usefulness of the proposed index compared to the existing index is demonstrated.

Abstract Image

衡量序方差表偏离对称程度的指数
为了分析具有相同行列序数分类的方形或然率表,本研究提出了一种使用新累积概率来衡量偏离对称模型程度的指数。建议的指数是基于 Cressie 和 Read 的幂发散或 Patil 和 Taillie 的多样性指数的加权平均值构建的。本研究推导出了拟议指数的插件估计器和拟议指数的近似置信区间。与现有指数的估算器相比,即使样本量不大,拟议指数的估算器也有望减少偏差。在条件对称模型下,拟议指数与现有指数相同。因此,假设条件对称模型的概率结构成立,就可以简单地比较拟议指数和现有指数的插件估计器的性能。通过数值示例和实际数据分析,证明了拟议指数与现有指数相比的实用性。
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来源期刊
Journal of the Korean Statistical Society
Journal of the Korean Statistical Society 数学-统计学与概率论
CiteScore
1.30
自引率
0.00%
发文量
37
审稿时长
3 months
期刊介绍: The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.
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