[Lecture]Xinbing Kong:Separating the common and idiosyncratic component without moment condition and on the weighted L1 solution path
Time: 15:00-16:00pm, Oct. 16th, 2020, Friday
Venue: Tencent meeting ID:139 794 622
Spreker:Xinbing Kong, Professor,Nanjing Audit University
Abstract:In large-dimensional factor analysis, existing methods, such as principal component analysis (PCA), assumed finite fourth moment of the idiosyncratic components, in order to derive the convergence rates of the estimated factor loadings and scores. However, in many areas, such as finance and macroeconomics, many variables are heavy-tailed. In this case, PCA-based estimators and their variations are not theoretically underpinned. In this paper, we investigate into the weighted L1 minimization on the factor loadings and scores, which amounts to assuming a temporal and cross-sectional quantile structure for panel observations instead of the mean pattern in $L_2$ minimization. Without any moment constraint on the idiosyncratic errors, we correctly identify the common and idiosyncratic components for each variable. We obtained the convergence rates of computationally feasible weighted $L_1$ minimization estimators via iteratively alternating the quantile regression cross-sectionally and serially. Bahardur representations for the estimated factor loadings and scores are provided under some mild conditions. In addition, a robust method is proposed to estimate the number of factors consistently. Simulation experiments checked the validity of the theory. Our analysis on a financial data set shows the superiority of the proposed method over other state-of-the-art methods. A joint work with He Yong, Yu Long and Zhang Xinsheng.
Speaker’s Bio:孔新兵，南京审计大学教授、香港科技大学博士。研究领域为经济统计、数理统计、网络数据统计。孔新兵教授主持自然科学基金面上、青年项目各1项；教育部人文社科项目1项。在统计学顶级期刊JASA、AOS、 Biometrika以及计量经济学顶级期刊JOE发表论文十余篇。国际统计协会当选会员(ISI elected member)，现任中国现场统计研究会高维数据统计分会理事。
