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<p>In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful when the nonzero signal in mean vectors is weakly dense with almost the same sign. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-norm-based test statistic exhibits favorable properties in terms of both size and power.</p>

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Test for High-Dimensional Mean Vectors via the Weighted L2-norm

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Jianghao Li,
  • Zhenzhen Niu,
  • Shizhe Hong,
  • Zhidong Bai

摘要

In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted \(L_2\) L 2 -norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful when the nonzero signal in mean vectors is weakly dense with almost the same sign. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted \(L_2\) L 2 -norm-based test statistic exhibits favorable properties in terms of both size and power.