Discretization error for the maximum of a Gaussian field |
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Affiliation: | 1. Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States;2. Departments of Statistics and Mathematics, The Ohio State University, Columbus, OH 43210, United States |
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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). |
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Keywords: | Gaussian field Field maximum Discretization error Slepian model |
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