<p>In this paper, we introduce a novel independence test for two random vectors. The test is grounded in a novel metric referred to as characteristic covariance, which completely captures the independence of random vectors. The metric we propose possesses some appealing features: (i) it is non-negative, equal to zero, if and only if independence holds; (ii) it is nonparametric and model-free, which makes the metric robust to outliers or heavy-tailed data; (iii) the new method is applicable for detecting dependence in high-dimensional settings. Moreover, its empirical version is easy to implement and well-suited for independence testing. Theoretically, we prove the convergence of the proposed test under both the null and alternative hypotheses. Under the null hypothesis, it converges in distribution to a quadratic form. Under the alternative hypothesis, it is asymptotically normal. Simulation studies and real-data analyses demonstrate that the test based on the characteristic covariance is effective in detecting dependences.</p>

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Testing for independence in high dimensions based on characteristic covariance

  • Xu Li,
  • Bingcan Wang,
  • Baoxue Zhang

摘要

In this paper, we introduce a novel independence test for two random vectors. The test is grounded in a novel metric referred to as characteristic covariance, which completely captures the independence of random vectors. The metric we propose possesses some appealing features: (i) it is non-negative, equal to zero, if and only if independence holds; (ii) it is nonparametric and model-free, which makes the metric robust to outliers or heavy-tailed data; (iii) the new method is applicable for detecting dependence in high-dimensional settings. Moreover, its empirical version is easy to implement and well-suited for independence testing. Theoretically, we prove the convergence of the proposed test under both the null and alternative hypotheses. Under the null hypothesis, it converges in distribution to a quadratic form. Under the alternative hypothesis, it is asymptotically normal. Simulation studies and real-data analyses demonstrate that the test based on the characteristic covariance is effective in detecting dependences.