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On identifiability and consistency of the nugget in Gaussian spatial process models

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  • Wenpin Tang
  • Lu Zhang
  • Sudipto Banerjee

Abstract

Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or microscale variability, and is called the ‘nugget’. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in‐fill asymptotics, that is the sample size increases within a sampling domain that is bounded. Our work extends results in fixed domain asymptotics for spatial models without the nugget. More specifically, we establish the identifiability of parameters in the Matérn covariogram and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget. We also present simulation studies to demonstrate the role of the identifiable quantities in spatial interpolation.

Suggested Citation

  • Wenpin Tang & Lu Zhang & Sudipto Banerjee, 2021. "On identifiability and consistency of the nugget in Gaussian spatial process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1044-1070, November.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:5:p:1044-1070
    DOI: 10.1111/rssb.12472
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    References listed on IDEAS

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    Cited by:

    1. David B. Dunson & Hau‐Tieng Wu & Nan Wu, 2022. "Graph based Gaussian processes on restricted domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 414-439, April.

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