171 – New Nonparametric Methods for Correlated Data
Nonparametric Covariance Estimation with Shrinkage Toward Stationary Models
Tayler Blake
Information Control Company
Yoonkyung Lee
The Ohio State University
The covariance matrix of a p-dimensional vector of repeated measurements contains as many as p(p+1)/2 constrained parameters. In addition to the issue of high dimensionality, estimating a covariance matrix is difficult due to positive-definite constraints imposed on estimates. To mitigate these challenges, the use of generalized linear models for the mean of a random variable has been extended to estimation of the covariance matrix. Analogous to application of a link function to the mean, the modified Cholesky decomposition provides an unconstrained parameterization of the covariance matrix which guarantees that estimates are positive-definite. The components of the modified Cholesky decomposition can be interpreted as a particular set of regression coefficients and error variances. To accommodate irregular or sparsely sampled data, we employ bivariate smoothing splines to generalize the regression models to its functional analog. We propose a general framework for regularized covariance estimation which allows for a flexible notion of parsimony in estimated models. We evaluate performance via simulation studies and discuss its application to Kenward's cattle data (1987).