Band-Width Selection for High-Dimensional Covariance Matrix Estimation

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Yumou Qiu*+ and Song Xi Chen
• Companies: and Peking University and Iowa State University
• Keywords: Bandable covariance ; High dimensionality ; M-estimation ; Nonparametric ; Large p, small n ; Ratio-consistency

Abstract

The banding estimator of Bickel and Levina (2008a) and its tapering version of Cai, Zhang and Zhou (2010) are the most significant high dimensional covariance estimator. Both estimators require choosing a band width parameter. We propose a band width selector for the banding covariance estimator by minimizing an empirical estimate of the expected squared Frobenius norms of the estimation error matrix. The ratio consistency of the band width selector to the underlying band width is established. We also provide a lower bound for the coverage probability of the underlying band width being contained in an interval around the band width estimate. An extension to the band width selection for the tapering estimator is made. Numerical simulations and a case study on sonar spectrum data are conducted to confirm and demonstrate the proposed band width estimation approaches.