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Testing conditional independence and homogeneity in large sparse three‐way tables using conditional distance covariance
Author(s) -
Zhang Qingyang,
Tinker Jian
Publication year - 2019
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.244
Subject(s) - contingency table , conditional independence , conditional variance , covariance , mathematics , homogeneity (statistics) , statistics , categorical variable , statistic , test statistic , statistical hypothesis testing , econometrics , volatility (finance) , autoregressive conditional heteroskedasticity
Conditional independence test for three‐way contingency tables is a classic problem in multivariate statistics. Traditional methods including Cochran–Mantel–Haenszel test and conditional mutual information test are powerful under sufficient sample size; however, in sparse settings, these methods may fail to detect the association due to the violation of normality assumption. In this paper, we propose to use a recently developed measure, namely, conditional distance covariance, to test conditional independence in large sparse R × C × K tables. We derive the explicit formula of conditional distance covariance between three categorical variables, and we suggest a maximum‐type statistic for hypothesis testing. In addition, we introduce a new statistic based on distance covariance to test homogeneity in three‐way tables. We conduct an extensive simulation study to illustrate the superiority of our method to the existing ones.