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Motivated by the importance of measuring the association between the responseand predictors in high dimensional data, In this article, we propose a new meanvariance test of independence between a categorical random variable and acontinuous one based on mean variance index. The mean variance index is zero ifand only if two variables are independent. Under the independence, we derive anexplicit form of its asymptotic null distribution, which provides us with anefficient and fast way to compute the empirical p-value in practice. The numberof classes of the categorical variable is allowed to diverge slowly to theinfinity. It is essentially a rank test and thus distribution-free. Noassumption on the distributions of two random variables is required and thetest statistic is invariant under one-to-one transformations. It is resistentto heavy-tailed distributions and extreme values. We assess its performance byMonte Carlo simulations and demonstrate that the proposed test achieves ahigher power in comparison with the existing tests. We apply the proposed MVtest to a high dimensional colon cancer gene expression data to detect thesignificant genes associated with the tissue syndrome.

A Distribution-Free Test of Independence and Its Application to Variable Selection