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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 
 

 

Extrapolation of stationary random fields via level sets


Authors: A. Das, V. Makogin and E. Spodarev
Journal: Theor. Probability and Math. Statist. 106 (2022), 85-103
MSC (2020): Primary 54C40, 14E20; Secondary 46E25, 20C20
DOI: https://doi.org/10.1090/tpms/1166
Published electronically: May 16, 2022
MathSciNet review: 4438445
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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.


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Additional Information

A. Das
Affiliation: Institute of Stochastics, University of Ulm, Germany
Email: abhinabdas7@gmail.com

V. Makogin
Affiliation: Institute of Stochastics, University of Ulm, Germany
Email: vitalii.makogin@uni-ulm.de

E. Spodarev
Affiliation: Institute of Stochastics, University of Ulm, Germany
Email: evgeny.spodarev@uni-ulm.de

Keywords: Stationary random field, Gaussian random field, extrapolation, linear prediction, excursion, level set, second order cone programming, quadratically constrained quadratic problem
Received by editor(s): July 31, 2021
Accepted for publication: October 18, 2021
Published electronically: May 16, 2022
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv