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A Fused Lasso Approach to Nonstationary Spatial Covariance Estimation

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  • Ryan J. Parker

    (SAS Institute)

  • Brian J. Reich

    (North Carolina State University)

  • Jo Eidsvik

    (Norwegian University of Science and Technology)

Abstract

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.

Suggested Citation

  • Ryan J. Parker & Brian J. Reich & Jo Eidsvik, 2016. "A Fused Lasso Approach to Nonstationary Spatial Covariance Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 569-587, September.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:3:d:10.1007_s13253-016-0251-8
    DOI: 10.1007/s13253-016-0251-8
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    3. Joaquim Henriques Vianna Neto & Alexandra M. Schmidt & Peter Guttorp, 2014. "Accounting for spatially varying directional effects in spatial covariance structures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 103-122, January.
    4. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    5. Luke Bornn & Gavin Shaddick & James V. Zidek, 2012. "Modeling Nonstationary Processes Through Dimension Expansion," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 281-289, March.
    6. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848, September.
    7. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    8. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Nan‐Jung Hsu & Ya‐Mei Chang & Hsin‐Cheng Huang, 2012. "A group lasso approach for non‐stationary spatial–temporal covariance estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 12-23, February.
    9. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    10. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
    11. Brian J. Reich & Howard H. Chang & Kristen M. Foley, 2014. "A spectral method for spatial downscaling," Biometrics, The International Biometric Society, vol. 70(4), pages 932-942, December.
    12. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296, May.
    13. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    14. Finley, Andrew O. & Sang, Huiyan & Banerjee, Sudipto & Gelfand, Alan E., 2009. "Improving the performance of predictive process modeling for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2873-2884, June.
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