Multivariate piecewise linear interpolation of a random field

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

approximation

random field

sampling design

multivariate piecewise linear interpolator

Mathematical Statistics

matematisk statistik

Publication and Content Type

vet (subject category)

ovr (subject category)