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A distribution-free test of independence based on mean variance index

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  • Cui, Hengjian
  • Zhong, Wei

Abstract

A new test based on mean variance (MV) index is proposed for testing the independence between a categorical random variable Y and a continuous one X. The MV index can be considered as the weighted average of Cramér–von Mises distances between the conditional distribution functions of X given each class of Y and the unconditional distribution function of X. The MV index is zero if and only if X and Y are independent. The new MV test between X and Y enjoys several appealing merits. First, an explicit form of the asymptotic null distribution is derived under the independence between X and Y. It provides an efficient way to compute critical values and p-value. Second, no assumption on the distributions of two random variables is required and the new test statistic is invariant under one-to-one transformations of the continuous random variable. It is essentially a rank test and distribution-free, so it is resistant to heavy-tailed distributions and extreme values in practice. Monte Carlo simulations demonstrate its excellent finite-sample performance. In applications, the MV test is used in two high dimensional gene expression data to detect the significant genes associated with tumor types.

Suggested Citation

  • Cui, Hengjian & Zhong, Wei, 2019. "A distribution-free test of independence based on mean variance index," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 117-133.
  • Handle: RePEc:eee:csdana:v:139:y:2019:i:c:p:117-133
    DOI: 10.1016/j.csda.2019.05.004
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    References listed on IDEAS

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    1. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    2. Ruth Heller & Yair Heller & Malka Gorfine, 2013. "A consistent multivariate test of association based on ranks of distances," Biometrika, Biometrika Trust, vol. 100(2), pages 503-510.
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    Cited by:

    1. Xin Dang & Dao Nguyen & Yixin Chen & Junying Zhang, 2021. "A new Gini correlation between quantitative and qualitative variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1314-1343, December.

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