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Activity Number: 579
Type: Invited
Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
Sponsor: ENAR
Abstract #318391
Title: Robust Covariance Estimation for Approximate Factor Models
Author(s): Jianqing Fan and Weichen Wang* and Yiqiao Zhong
Companies: Princeton and Princeton and Princeton
Keywords: Robust Covariance Estimation ; Approximate Factor Model ; Heavy-tailed Distributions ; Perturbation Bound

Robust estimation of covariance matrices has been fundamental in statistics, especially when data are generated from heavy-tailed distributions. In this work, we study robust estimation under the approximate factor model with both observed and unobserved factors. For both situations, we proposed novel frameworks to first get an initial covariance estimation, and then refine it by recovering the low-rank structure and thresholding the sparse error matrix. We proved that once the initial matrix estimator is good enough to maintain the element-wise optimal rate, the whole procedure will generate an estimated covariance with desired properties. Therefore, for data with only bounded fourth moment, we proposed to use Huber loss minimization to obtain the initial covariance estimator. Whereas if data are generated by sub-Gaussian or elliptical distribution, the corresponding sample covariance and Kendall's tau estimators are ideal for the initial estimation. Therefore we thoroughly extend robust factor analysis. As a side product, perturbation bound in max norm for eigenvectors are invented. All conclusions are demonstrated by exhaustive simulations and real data analyses.

Authors who are presenting talks have a * after their name.

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