A family of association measures for 2 x 2 contingency tables based on the φ-divergence
A family of association measures for 2 x 2 contingency tables based on the φ-divergence
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DOI：
10.1016/j.stamet.2015.12.002
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发表时间：
2016-05-01
影响因子：
--
通讯作者：
Kateri, Maria
中科院分区：
文献类型：
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作者：
Espendiller, Michael;Kateri, Maria
优势比是 2 x 2 列联表中关联的主要度量，出于推理目的，通常在对数尺度上考虑。在信息论设置下，它与 Kullback-Leibler 散度相关。考虑到广义的散度族，即 phi 散度，针对 2 x 2 列联表导出替代关联度量。研究了它们的性质并开发了渐近推理。对于这个家族的一些成员，估计的关联测量在存在采样零的情况下仍然是有限的，而对于这些成员的子集，这些测量的估计量也具有有限的方差。特别关注功率发散，它是一个参数族。进一步讨论了其参数 A 在渐近置信区间的覆盖概率和平均相对长度方面的作用。在特殊的概率表结构中，经典对数比值比的渐近置信区间的性能较差，建议使用与 lambda = 1/3 相对应的度量作为替代方案。 (C) 2016 Elsevier B.V. 保留所有权利。
The odds ratio is the predominant measure of association in 2 x 2 contingency tables, which, for inferential purposes, is usually considered on the log-scale. Under an information theoretic setup, it is connected to the Kullback-Leibler divergence. Considering a generalized family of divergences, the phi divergence, alternative association measures are derived for 2 x 2 contingency tables. Their properties are studied and asymptotic inference is developed. For some members of this family, the estimated association measures remain finite in the presence of a sampling zero while for a subset of these members the estimators of these measures have finite variance as well. Special attention is given to the power divergence, which is a parametric family. The role of its parameter A, in terms of the asymptotic confidence intervals' coverage probability and average relative length, is further discussed. In special probability table structures, for which the performance of the asymptotic confidence intervals for the classical log odds ratio is poor, the measure corresponding to lambda = 1/3 is suggested as an alternative. (C) 2016 Elsevier B.V. All rights reserved.