Hypothesis testing for band size detection of high-dimensional banded precision matrices

• 成果类型: Article
• 署名作者: An, Baiguo; Guo, Jianhua; Liu, Yufeng
• 署名单位: Capital University of Economics & Business; Northeast Normal University - China; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu006
• 发表日期: 2014
• 页码: 477483
• 关键词: large covariance matrices; selection; regularization

摘要

Many statistical analysis procedures require a good estimator for a high-dimensional covariance matrix or its inverse, the precision matrix. When the precision matrix is banded, the Cholesky-based method often yields a good estimator of the precision matrix. One important aspect of this method is determination of the band size of the precision matrix. In practice, crossvalidation is commonly used; however, we show that crossvalidation not only is computationally intensive but can be very unstable. In this paper, we propose a new hypothesis testing procedure to determine the band size in high dimensions. Our proposed test statistic is shown to be asymptotically normal under the null hypothesis, and its theoretical power is studied. Numerical examples demonstrate the effectiveness of our testing procedure.