This article is published in Environmetrics as a special issue on Spatio-Temporal Stochastic Modelling (METMAV), edited by Wenceslao González-Manteiga and Rosa M. Crujeiras, University of Santiago de Compostela, Spain.
Special Issue Paper
A group lasso approach for non-stationary spatial–temporal covariance estimation†
Article first published online: 31 AUG 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Special Issue: Spatio-Temporal Stochastic Modelling. (METMAV)
Volume 23, Issue 1, pages 12–23, February 2012
How to Cite
Hsu, N.-J., Chang, Y.-M. and Huang, H.-C. (2012), A group lasso approach for non-stationary spatial–temporal covariance estimation. Environmetrics, 23: 12–23. doi: 10.1002/env.1130
- Issue published online: 16 JAN 2012
- Article first published online: 31 AUG 2011
- Manuscript Accepted: 9 JUL 2011
- Manuscript Revised: 26 MAY 2011
- Manuscript Received: 17 NOV 2010
- coordinate descent;
- Frobenius loss;
- group lasso;
- Kalman filter;
- penalized least squares;
- spatial prediction
We develop a new approach for modeling non-stationary spatial–temporal processes on the basis of data sampled at fixed locations over time. The approach applies a basis function formulation and a constrained penalized least squares method recently proposed for estimating non-stationary spatial-only covariance functions. In this article, we further incorporate the temporal dependence into this framework and model the spatial–temporal process as the sum of a spatial–temporal stationary process and a linear combination of known basis functions with temporal dependent coefficients. A group lasso penalty is devised to select the basis functions and estimate the parameters simultaneously. In addition, a blockwise coordinate descent algorithm is applied for implementation. This algorithm computes the constrained penalized least squares solutions along a regularization path very rapidly. The resulting dynamic model has a state-space form, thereby the optimal spatial–temporal predictions can be computed efficiently using the Kalman filter. Moreover, the methodology is applied to a wind speed data set observed at the western Pacific Ocean for illustration. Copyright © 2011 John Wiley & Sons, Ltd.