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Discretization error for the maximum of a Gaussian field

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  • Azaïs, Jean-Marc
  • Chassan, Malika

Abstract

The paper considers the difference between (a) the true maximum of a Gaussian field on a square and (b) its maximum on a regular grid. This difference is called the discretization error. A kind of Slepian model is used to study the behavior of the field around the location of the maximum. We show that the normalized discretization error can be bounded by a quantity that converges to a uniform variable, depending on the Hessian matrix at the point of the maximum. The bound is applied to simulated and real data (satellite positioning data).

Suggested Citation

  • Azaïs, Jean-Marc & Chassan, Malika, 2020. "Discretization error for the maximum of a Gaussian field," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 545-559.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:545-559
    DOI: 10.1016/j.spa.2019.02.002
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    References listed on IDEAS

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    1. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
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    Cited by:

    1. Elena Di Bernardino & Céline Duval, 2022. "Statistics for Gaussian random fields with unknown location and scale using Lipschitz‐Killing curvatures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 143-184, March.

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