title: Hypothesis testing for band size detection of high-dimensional banded precision matrices.
abstract: 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.
authors.affiliation: School of Statistics, Capital University of Economics and Business, Beijing 100070, China, anbg200@gmail.com.
authors.forename: Baiguo
authors.initials: B
authors.lastname: An
authors.affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China, jhguo@nenu.edu.cn.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Guo
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A., yfliu@email.unc.edu.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Liu
keywords: Band size; Banded matrix; Cholesky decomposition; Covariance matrix; High-dimensional hypothesis test; Multiple comparison; Precision matrix