Robust Large Covariance Estimation for Heavy-tailed Factor Models
报告人： Weichen Wang
We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high-level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework allows us to exploit conditional sparsity covariance structure for the heavy-tailed data. In particular, for the elliptical distribution, we propose a robust estimator based on the marginal and spatial Kendall’s tau to satisfy these conditions. For general heavy-tailed distribution, we resort to a newly developed maximum norm perturbation bound of eigenvectors to show that robust methodology can be applied as well. In addition, we study conditional graphical model under the same framework. The technical tools developed in this paper are of general interest to high-dimensional principal component analysis. Thorough numerical results are also provided to back up the developed theory.
About the Speaker:
Dr. Weichen Wang graduated from the department of Operations Research and Financial Engineering at Princeton University in 2016. His research is a combination of econometrics and statistics, focusing on applying high dimensional inference, semi-parametric modeling, robust techniques and machine learning on the low-rank plus sparse covariance structure, or factor model in financial econometrics. Before his PhD, Dr. Wang received his bachelor's degree from Tsinghua University in 2011, majoring in Mathematics and Physics. He is currently a quantitative researcher at Two Sigma Investments.