title: Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor.
abstract: In this article, we propose a computationally efficient approach to estimate (large)p-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of sizen. To do this, we construct the estimator based on ak-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerably faster than many existing methods and only requires inversion of (k+ 1)-dimensional covariance matrices. The resulting estimator is positive definite as long ask < n(wherepcan be larger thann). We make connections between this approach and banding the Cholesky factor of the modified Cholesky decomposition of the inverse covariance matrix (Wu and Pourahmadi, 2003) and show that the maximum likelihood estimator of thek-band partial autocorrelation matrix is the same as thek-band inverse Cholesky factor. We evaluate our estimator via extensive simulations and illustrate the approach using high-dimensional sonar data.
authors.affiliation: wang.yanpin@scrippshealth.org , Scripps Health, La Jolla, CA 92037.
authors.forename: Y
authors.initials: Y
authors.lastname: Wang
authors.affiliation: mjdaniels@austin.utexas.edu , University of Texas at Austin, Austin, TX 78712.
authors.forename: M J
authors.initials: MJ
authors.lastname: Daniels
keywords: High dimensional covariance matrices; Hypothesis testing; Partial autocorrelations