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Theory of Probability and Mathematical Statistics



Extrapolation of stationary random fields via level sets

A. Das, V. Makogin and E. Spodarev

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Abstract: In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric difference of these sets under the condition that the univariate distributions of the predictor and of the field itself coincide. We illustrate the new approach on Gaussian random fields.

Keywords: Stationary random field, Gaussian random field, extrapolation, linear prediction, excursion, level set, second order cone programming, quadratically constrained quadratic problem

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