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Modeling Nonstationary Processes Through Dimension Expansion


  • Luke Bornn
  • Gavin Shaddick
  • James V. Zidek


In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher-dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multidimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed dataset historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:281-289
    DOI: 10.1080/01621459.2011.646919

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    1. repec:spr:stabio:v:9:y:2017:i:2:d:10.1007_s12561-016-9150-3 is not listed on IDEAS
    2. repec:bla:jorssc:v:66:y:2017:i:5:p:919-939 is not listed on IDEAS
    3. repec:bla:biomet:v:73:y:2017:i:3:p:759-768 is not listed on IDEAS
    4. Yi Liu & Gavin Shaddick & James V. Zidek, 0. "Incorporating High-Dimensional Exposure Modelling into Studies of Air Pollution and Health," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-23.
    5. repec:eee:csdana:v:117:y:2018:i:c:p:138-153 is not listed on IDEAS
    6. Raphaƫl Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    7. 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.

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