Discretization error for the maximum of a Gaussian field

Jean-Marc Azaïs and Malika Chassan

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 545-559

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).

Keywords: Gaussian field; Field maximum; Discretization error; Slepian model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.02.002

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