Conditional Sparsity in Large Covariance Matrix Estimation

• Activity Number: 280
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jianqing Fan*+ and Yuan Liao and Martina Mincheva
• Companies: Princeton University and University of Maryland and Princeton University
• Keywords: Factor model ; Principal Component Analysis ; Thresholding ; POET ; Large covariance matrix

Abstract

Large covariance matrix plays a central role in finance and economics as well as statistical inferences. Popular regularization methods of exploiting sparsity are not directly applicable to many financial problems such as portfolio allocations and risk managements and biological problem such as false discovery rate controls. The methods based on the strict factor models is too restrictive. By imposing conditional sparsity, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We deal with the situations under which the conditioning factors are unobservable. The factor loading matrix and realized factors are estimated by principal component analysis. We estimate the sparse covariance using the adaptive thresholding technique, taking into account the fact that direct observations of the idiosyncratic noises are unavailable. The impact of high dimensionality is then studied theoretically and confirmed by simulation experiments. The applications to a few important statistical inferences will be used to illustration the methodological power of the proposed method.