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Open AccessArticle

A Class of Association Measures for Categorical Variables Based on Weighted Minkowski Distance

Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA
Entropy 2019, 21(10), 990; https://doi.org/10.3390/e21100990
Received: 16 August 2019 / Revised: 28 September 2019 / Accepted: 10 October 2019 / Published: 11 October 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
Measuring and testing association between categorical variables is one of the long-standing problems in multivariate statistics. In this paper, I define a broad class of association measures for categorical variables based on weighted Minkowski distance. The proposed framework subsumes some important measures including Cramér’s V, distance covariance, total variation distance and a slightly modified mean variance index. In addition, I establish the strong consistency of the defined measures for testing independence in two-way contingency tables, and derive the scaled forms of unweighted measures. View Full-Text
Keywords: dependence measure; categorical variable; Minkowski distance; sparse contingency table; total variation distance; mean variance index dependence measure; categorical variable; Minkowski distance; sparse contingency table; total variation distance; mean variance index
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Zhang, Q. A Class of Association Measures for Categorical Variables Based on Weighted Minkowski Distance. Entropy 2019, 21, 990.

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