Spherically Invariant Vector Random Fields in Space and Time

Abstract

This paper is concerned with spherically invariant or elliptically contoured vector random fields in space and/or time, which are formulated as scale mixtures of vector Gaussian random fields. While a spherically invariant vector random field may or may not have second-order moments, a spherically invariant second-order vector random field is determined by its mean and covariance matrix functions, just like the Gaussian one. This paper explores basic properties of spherically invariant second-order vector random fields, and proposes an efficient approach to develop covariance matrix functions for such vector random fields.

Logistic vector random fields with logistic direct and cross covariances

“…However, there may not exist a non-Gaussian, such as a χ 2 (Ma, 2011c), log-Gaussian, skew-Gaussian, or K-distributed random field with C(x 1 , x 2 ) as its covariance matrix function. The logistic vector random field developed here belongs to the family of elliptically contoured (spherically invariant) vector random fields (Du and Ma, 2011;Ma, 2011a), and thus allows for any given correlation structure. The rest of this paper is organized as follows.…”