Multivariate piecewise linear interpolation of a random field
2011 (English)Manuscript (preprint) (Other academic)
We consider a multivariate piecewise linear interpolation of a continuous random field on a-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear 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 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
2011. Vol. 1102.1871
approximation, random field, sampling design, multivariate piecewise linear interpolator
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-60995OAI: oai:DiVA.org:umu-60995DiVA: diva2:565244