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Piecewise multilinear interpolation of a random field
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 45, no 4, 945-959 p.Article in journal (Refereed) Published
Abstract [en]

We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

Place, publisher, year, edition, pages
2013. Vol. 45, no 4, 945-959 p.
Keyword [en]
Approximation, random field, piecewise-multilinear interpolator, sampling design
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-81408DOI: 10.1239/aap/1386857852ISI: 000330201100004OAI: oai:DiVA.org:umu-81408DiVA: diva2:655037
Funder
Swedish Research Council, 2009-4489
Available from: 2013-10-09 Created: 2013-10-09 Last updated: 2017-12-06Bibliographically approved

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Abramowicz, KonradSeleznjev, Oleg
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