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On Information About Covariance Parameters in Gaussian Matérn Random Fields

Author

Listed:
  • Victor De Oliveira

    (The University of Texas at San Antonio)

  • Zifei Han

    (University of International Business and Economics)

Abstract

The Matérn family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications, the smoothness parameter is set at an arbitrary value. This practice is due partly to computational challenges faced when attempting to estimate all covariance parameters and partly to unqualified claims in the literature stating that geostatistical data have little or no information about the smoothness parameter. This work critically investigates this claim and shows it is not true in general. Specifically, it is shown that the information the data have about the correlation parameters varies substantially depending on the true model and sampling design and, in particular, the information about the smoothness parameter can be large, in some cases larger than the information about the range parameter. In light of these findings, we suggest to reassess the aforementioned practice and instead establish inferences from data-based estimates of both range and smoothness parameters, especially for strongly dependent non-smooth processes observed on irregular sampling designs. A data set of daily rainfall totals is used to motivate the discussion and gauge this common practice.

Suggested Citation

  • Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:4:d:10.1007_s13253-022-00510-5
    DOI: 10.1007/s13253-022-00510-5
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    References listed on IDEAS

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    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. Peter Diggle & Søren Lophaven, 2006. "Bayesian Geostatistical Design," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 53-64, March.
    3. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    4. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    5. C. G. Kaufman & B. A. Shaby, 2013. "The role of the range parameter for estimation and prediction in geostatistics," Biometrika, Biometrika Trust, vol. 100(2), pages 473-484.
    6. Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
    7. Stein, Michael L., 1993. "A simple condition for asymptotic optimality of linear predictions of random fields," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 399-404, August.
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