Nonparametric Covariance Estimation with Shrinkage Toward Stationary Models

• Activity Number: 104
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Yoonkyung Lee*+ and Tayler Blake
• Companies: Ohio State University and Ohio State University
• Keywords: bivariate smoothing ; covariance ; functional data ; longitudinal data ; penalization

Abstract

With high dimensional longitudinal and functional data becoming much more common, there is a strong need for methods of estimating large covariance matrices. Estimation is made difficult by the instability of sample covariance matrices in high dimensions and a positive-definite constraint we desire to impose on estimates. A Cholesky decomposition of the covariance matrix allows for parameter estimation via unconstrained optimization as well as a statistically meaningful interpretation of the parameter estimates. Regularization improves stability of covariance estimates in high dimensions, as well as in the case where functional data are sparse and individual curves are sampled at different and possibly unequally spaced time points.

Treating covariance estimation as bivariate smoothing, we propose novel covariance penalties within regularization framework, which are designed to yield natural null models presented in the literature for stationarity or short-term dependence. These penalties are expressed in terms of variation in continuous time lag and its orthogonal direction. We present numerical results and data analysis to illustrate the utility of the proposed method.