发表机构
Tsinghua University; Shanghai University of Finance and Economics; Ruhr-Universität Bochum（清华大学; 上海财经大学; 波鸿鲁尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究高维典范二阶U-统计量最大值的联合推断，提出以联合符号高斯二次混沌为目标的一般逼近定理，识别有效秩驱动的相变，并引入避免特征系统估计的高斯乘子自助法，通过应用和模拟验证其有效性。
AI 中文摘要
我们研究高维下二阶典范U-统计量最大值的联合推断。退化性使得二次波动占主导，因此即使在精确方差归一化后，普通高斯校准也可能失效。我们证明合适的一般目标是联合符号高斯二次混沌，并建立允许不定核的一般逼近结果。一般反集中界对于高维推断过于粗糙，我们在额外谱结构下获得更精确的界。我们还识别出一个由有效秩驱动的相变，从非高斯符号混沌最大值转变为其协方差匹配的高斯对应。为可行推断，我们提出一种避免估计特征系统的高斯乘子自助法，并证明其有效性。两个应用和大量数值模拟进一步展示了所提框架的范围和实际性能。
英文摘要
We study simultaneous inference for maxima of canonical order-two $U$-statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibration can fail even after exact variance normalization. We show that the appropriate general target is a joint signed Gaussian quadratic chaos and establish a general approximation result that permits indefinite kernels. The general anti-concentration bound is too crude for high-dimensional inference, and we obtain sharper bounds under additional spectral structure. We also identify a phase transition from a non-Gaussian signed-chaos maximum to its covariance-matched Gaussian counterpart driven by the effective rank. For feasible inference, we propose a Gaussian multiplier bootstrap that avoid estimating eigensystems, and establish its validity. Two applications and extensive numerical simulations further illustrate the scope and practical performance of the proposed framework.
