Covariance-Assisted Screening and Estimation

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Tracy Ke*+ and Jiashun Jin and Jianqing Fan
• Companies: Princeton University and Carnegie Mellon University and Princeton University
• Keywords: asymptotic minimaxity ; multivariate screening ; phase diagram ; sparsity ; variable selection ; change point

Abstract

Motivated by examples include the long-memory time series and change-point problem, we considered variable selection in linear regressions where the Gram matrix is non-sparse but sparsifiable by a finite-order linear filter.

We proposed a new procedure called the Covariance Assisted Screening and Estimation (CASE). CASE is a two-stage Screen and Clean procedure, where it first applies a linear filtering to sparsify the Gram (covariance) matrix, and then uses the sparse graph induced by the new covariance matrix to conduct multivariate screening without visiting all submodels, and finally decomposes the original variable selection problem into many separated small-size subproblems. A new technique called patching was also introduced to address the issue of information leakage caused by linear filtering.

We showed that in a broad class of situations where the Gram matrix is non-sparse but sparsifiable, CASE achieves the optimal rate of convergence in Hamming distance between the true coefficient vector and the estimated one. The optimal rates are calculated for the long-memory time series model and the change-point model.