论文标题
在高维因子模型中测试通过自举样品协方差矩阵测试常见因素的数量
Testing the number of common factors by bootstrapped sample covariance matrix in high-dimensional factor models
论文作者
论文摘要
本文研究了引导程序对在高维因子结构下样品协方差矩阵的特征值分布的影响。我们为在轻度条件下的自举样品协方差矩阵的顶部特征值提供渐近分布。引导程序后，在适当的缩放和集中化后，由共同因素驱动的尖刺特征值将微弱地汇聚到高斯极限。但是，最大的非尖刺特征值主要取决于自举重新采样权重的顺序统计，并遵循极端的价值分布。基于尖刺和非刺激特征值的不同行为，我们提出了创新方法来测试常见因素的数量。通过广泛的数值和经验研究指示，所提出的方法在弱因子和横截面相关的误差的存在下可靠而令人信服地表现出色。我们的技术详细信息有助于具有跨越腐烂的密度和无界支撑或一般椭圆形分布的尖峰协方差模型的随机矩阵理论。
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.
