【学术讲座】Testing the number of common factors by bootstrapped sample covariance matrix in high-dimensional factor models

发布者:统计与数据科学学院发布时间:2022-10-31浏览次数:1070

【专家简介】虞龙,现为上海财经大学统计与管理学院金融统计与风险管理系助理教授。他在20206月于复旦大学管理学院统计学系概率论与数理统计专业获得理学博士学位,20209月至20229月在新加坡国立大学统计与数据科学系从事博士后研究工作。他的主要研究方向是因子模型、高维数据分析、随机矩阵理论等。其主要研究成果发表于统计学与计量经济学的国际著名期刊Journal of Econometrics, Journal of Business and Economic Statistics, Bernoulli, Journal of Multivariate Statistics等。

【报告摘要】This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under the  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 via proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by order statistics of 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. According to the simulations and a real data example, the proposed methods are the only ones performing 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.

腾讯会议号:398-900-453

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