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<p>Several notions of multivariate symmetry exist including spherical, elliptical, diagonal, and angular symmetry, in decreasing order of stringency. We present tests of high dimensional diagonal symmetry based on a new dissimilarity index and the Energy statistic. Based on the lower bound of the Euclidean distance, the dissimilarity index exploits the concentration phenomenon in high dimensions. We show that testing diagonal symmetry is equivalent to testing the equality of two distributions. We obtain the asymptotic null and alternative distributions of the statistic and prove that the new test is consistent. One can also use the same methodology to test for high- dimensional angular symmetry. We apply the testing methods for diagonal symmetry to two microarray datasets.</p>

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Testing high dimensional diagonal symmetry

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • Yong Wang,
  • Reza Modarres

摘要

Several notions of multivariate symmetry exist including spherical, elliptical, diagonal, and angular symmetry, in decreasing order of stringency. We present tests of high dimensional diagonal symmetry based on a new dissimilarity index and the Energy statistic. Based on the lower bound of the Euclidean distance, the dissimilarity index exploits the concentration phenomenon in high dimensions. We show that testing diagonal symmetry is equivalent to testing the equality of two distributions. We obtain the asymptotic null and alternative distributions of the statistic and prove that the new test is consistent. One can also use the same methodology to test for high- dimensional angular symmetry. We apply the testing methods for diagonal symmetry to two microarray datasets.