Extrapolation of Stationary Random Fields

TL;DR

This paper introduces statistical methods for extrapolating stationary random fields, including kriging for square integrable fields and new techniques for heavy-tailed stable fields, expanding the toolkit for spatial data analysis.

Contribution

It presents new extrapolation methods for stable fields and generalizes kriging techniques to non-Gaussian, heavy-tailed random fields.

Findings

Kriging techniques for square integrable fields are outlined.

New extrapolation methods for stable, heavy-tailed fields are described.

Properties of these methods are discussed.

Abstract

We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.