Piecewise multilinear interpolation of a random field
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
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.
Approximation, random field, piecewise-multilinear interpolator, sampling design
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-81408DOI: 10.1239/aap/1386857852OAI: oai:DiVA.org:umu-81408DiVA: diva2:655037
FunderSwedish Research Council, 2009-4489