协方差矩阵
数学
协方差矩阵的估计
统计
因子分析
因子(编程语言)
协方差
样品(材料)
计量经济学
应用数学
计算机科学
物理
热力学
程序设计语言
作者
Lei Yu,Peng Zhao,Wang Zhou
标识
DOI:10.1080/01621459.2024.2346364
摘要
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions.
科研通智能强力驱动
Strongly Powered by AbleSci AI