Estimating Spatial Covariance Using Penalized Likelihood with Weighted L1 Penalty

• Activity Number: 355
• Type: Invited
• Date/Time: Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statisticians in Defense and National Security
• Author(s): Zhengyuan Zhu*+ and Yufeng Liu
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: LASSO ; Choleski Decomposition ; Sparsity ; Spatial statistics ; Spatial autoregression model

Abstract

In spatial statistics, estimation of large covariance matrix is of great importance because of its role in spatial prediction and design. The classical approach typically assumes that the spatial process is stationary and the covariance function takes some well-known parametric form, and estimates the parameters of the covariance functions using likelihood based methods. When data is available in both space and time, and the spatial stationarity assumption is not reasonable, sample covariance has been used to estimate the spatial covariance matrix. In this paper we study the covariance estimation problem for a class of nonstationary spatial autoregressive model. By exploiting the sparsity structure in the inverse covariance matrix, we show that a LASSO type approach gives improved covariance estimator measured by several criteria.