Covariance Regularization in Nonstationary Spatial Models

• Activity Number: 344
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ryan Parker*+ and Brian Reich and Jo Eidsvik
• Companies: North Carolina State University and North Carolina State University and Norwegian University of Science and Technology
• Keywords: nonstationary ; spatial ; penalized likelihood ; fused lasso ; spacious

Abstract

Estimation of nonstationary covariance structures in spatial models is challenging due to the large number of parameters needed to represent the nonstationary covariance. We propose the use of a penalized likelihood for the Paciorek and Schervish (2006) nonstationary covariance to regularize the estimation of a large number of covariance parameters. By using a parameter space on a discrete grid, this construction allows for the parameters in the nonstationary model to vary smoothly over space. We also demonstrate how the block composite likelihood of Eidsvik et al. (2014) allows for fast estimation of parameters in this model through the use of smaller covariance matrices and by exploiting parallelization of the block composite likelihood. Performance of this model is demonstrated with simulated and real data using the implementation of this method in the R package spacious.