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Comparing and selecting spatial predictors using local criteria

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  • Jonathan Bradley
  • Noel Cressie
  • Tao Shi

Abstract

Remote sensing technology for the study of Earth and its environment has led to “Big Data” that, paradoxically, have global extent but may be spatially sparse. Furthermore, the variability in the measurement error and the latent process error may not fit conveniently into the Gaussian linear paradigm. In this paper, we consider the problem of selecting a predictor from a finite collection of spatial predictors of a spatial random process defined on $$D$$ D , a subset of $$d$$ d -dimensional Euclidean space. Critically, we make no statistical distributional assumptions other than additive measurement error. In this nonparametric setting, one could use a criterion based on a validation dataset to select a spatial predictor for all of $$D$$ D . Instead, we propose local criteria based on validation data to select a predictor at each spatial location in $$D$$ D ; the result is a hybrid combination of the spatial predictors, which we call a locally selected predictor (LSP). We consider selection from a collection of some of the classical and more recently proposed spatial predictors currently available. In a simulation study, the relative performances of various LSPs, as well as the performance of each of the individual spatial predictors in the collection, are assessed. “Big Data” are always challenging, and here we apply LSP to a very large global spatial dataset of atmospheric $$\mathrm {CO}_{2}$$ CO 2 measurements. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
  • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:1-28
    DOI: 10.1007/s11749-014-0415-1
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    References listed on IDEAS

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    1. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    2. 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.
    3. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    4. Hai Nguyen & Noel Cressie & Amy Braverman, 2012. "Spatial Statistical Data Fusion for Remote Sensing Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1004-1018, September.
    5. Chen, Yin-Ping & Huang, Hsin-Cheng & Tu, I-Ping, 2010. "A new approach for selecting the number of factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2990-2998, December.
    6. 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.
    7. 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.
    8. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    9. 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.
    10. Hua Liang & Hulin Wu & Guohua Zou, 2008. "A note on conditional aic for linear mixed-effects models," Biometrika, Biometrika Trust, vol. 95(3), pages 773-778.
    11. Huang, Hsin-Cheng & Chen, Chun-Shu, 2007. "Optimal Geostatistical Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1009-1024, September.
    12. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    13. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
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    1. Zahra Barzegar & Firoozeh Rivaz, 2020. "A scalable Bayesian nonparametric model for large spatio-temporal data," Computational Statistics, Springer, vol. 35(1), pages 153-173, March.

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