高维椭圆因子模型中主特征值与特征向量的双样本检验

中文摘要 AI 辅助

主特征值和特征方向的变化为因子模型中的结构不稳定性提供了互补的诊断信息，但在重尾分布下，基于协方差的推断可能不可靠。我们针对高维椭圆因子模型，开发了关于迹归一化形状矩阵这些特征的双样本相等性检验。我们的方法将Tyler恒等式与正交化和交叉拟合相结合，以适应一般的位置和精度先导估计。我们推导出一种谱极限理论，该理论在无需对径向变量施加高阶矩假设的情况下，即可提供渐近有效的校准，从而允许两个总体具有不同的径向分布和因子秩。模拟实验表明，在重尾椭圆分布下，与基于协方差的基准方法相比，我们的方法具有良好的水平控制能力，并在调整后功效上有所提升。对标准普尔500指数股票收益率的应用说明了这些检验如何区分相对成分强度的变化与成分方向的变化。

英文摘要

Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S\&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.

发表机构

• Nankai University（南开大学）

机构由 AI 辅助整理，请以论文原文为准。