发表机构
Auburn University（奥本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出高维多元回归中结构变化检验的扫描方法，包括单点、多点及离散化多尺度扫描，并证明其渐近性质，应用于美国股票组合的因子暴露分析。
AI 中文摘要
我们研究了当响应维度与样本量成比例且预测变量数量固定时，多元线性回归中的结构变化检验问题。尽管这一问题与广泛领域的应用相关，但至今仍未被充分探索。所关注的备择假设允许在预测效应的指定线性对比中存在多个未知变化点。我们构造了一个基于最小二乘的Wald统计量，并用残差协方差估计量进行标准化，然后在候选变点分割上对其进行扫描。我们为单个和多个变点提出了灵活的分段扫描，以及一种降低计算成本的离散化多尺度扫描。当响应维度与样本量按比例发散时，我们建立了标准化统计量过程向中心化高斯过程的弱收敛性，从而为所有三种扫描提供了可实施的关键值。我们进一步刻画了它们在局部备择假设下的渐近功效，明确描述了信号、设计和高维比率如何决定极限功效。通过模拟研究检验了有限样本性能。我们将所提出的方法应用于美国股票投资组合的过滤和标准化收益率，以调查它们对Fama-French因子的暴露中存在的结构变化。
英文摘要
We study structural-change testing in multivariate linear regression when the response dimension is proportional to the sample size and the number of predictors is fixed. Despite its relevance to applications across a broad range of fields, this problem remains underexplored. The alternatives of interest allow multiple unknown changes in a prescribed linear contrast of the predictor effects. We construct a least-squares-based Wald statistic standardized by the residual covariance estimator and scan it over candidate change-point segmentations. We propose flexible segment scans for both single and multiple change points, together with a discretized multiscale scan that reduces the computational cost. When the response dimension and sample size diverge proportionally, we establish weak convergence of the normalized statistic process to a centered Gaussian process, yielding implementable critical values for all three scans. We further characterize their asymptotic power under local alternatives, explicitly describing how the signal, design, and high-dimensional aspect ratio determine the limiting power. The finite-sample performance is examined through simulation studies. We apply the proposed methods to filtered and standardized returns from U.S. equity portfolios to investigate structural changes in their exposures to the Fama--French factors.
