A Fused Lasso Approach to Nonstationary Spatial Covariance Estimation

  • Ryan J. ParkerEmail author
  • Brian J. Reich
  • Jo Eidsvik


Spatial data are increasing in size and complexity due to technological advances. For an analysis of a large and diverse spatial domain, simplifying assumptions such as stationarity are questionable and standard computational algorithms are inadequate. In this paper, we propose a computationally efficient method to estimate a nonstationary covariance function. We partition the spatial domain into a fine grid of subregions and assign each subregion its own set of spatial covariance parameters. This introduces a large number of parameters and to stabilize the procedure we impose a penalty to spatially smooth the estimates. By penalizing the absolute difference between parameters for adjacent subregions, the solution can be identical for adjacent subregions and thus the method identifies stationary subdomains. To apply the method to large datasets, we use a block composite likelihood which is natural in this setting because it also operates on a partition of the spatial domain. The method is applied to tropospheric ozone in the US, and we find that the spatial covariance on the west coast differs from the rest of the country.


Spatial statistics Nonstationary covariance Regularization Penalized likelihood 

Supplementary material

13253_2016_251_MOESM1_ESM.pdf (90 kb)
Supplementary material 1 (pdf 89 KB)


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Copyright information

© International Biometric Society 2016

Authors and Affiliations

  1. 1. SAS InstituteCaryUSA
  2. 2. North Carolina State UniversityRaleighUSA
  3. 3. Norwegian University of Science and TechnologyTrondheimNorway

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