Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data

Covariance Models for Latent Structure in Longitudinal Data

We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influence of covariates on the mean. Such analyses are particularly important in policy-related studies...

Supplementary Material: Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor

Fast covariance estimation for sparse functional data

Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing...

Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor

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 size n. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerabl...

Parallel Sparse Cholesky Factorization

Sparse matrix factorization plays an important role in many numerical algorithms. In this paper we describe a scalable parallel algorithm based on the Multifrontal Method. Computational experiments on a Parsytec CC system with 32 processors show that large sparse matrices can be factorized in only a few seconds.