Matérn Class Tensor-Valued Random Fields and Beyond

A normal distribution for tensor-valued random variables to analyze diffusion tensor MRI data

Diffusion Tensor MRI (DT-MRI) provides a statistical estimate of a symmetric 2 nd -order diffusion tensor, D, for each voxel within an imaging volume. We propose a new normal distribution, p(D) ~ exp(1/2 D:A:D), for a tensor random variable, D. The scalar invariant, D:A:D, is the contraction of a positive definite symmetric 4 th -order precision tensor, A , and D. A formal correspondence is est...

How big are the l ∞ - valued random fields ? ∗

In this paper we establish path properties and a generalized uniform law of the iterated logarithm (LIL) for strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random fields taking values in l∞-space.

Hölder Versions of Banach Space Valued Random Fields

For rather general moduli of smoothness ρ, like ρ(h)=h ln(c/h), we consider the Hölder spaces Hρ(B) of functions [0, 1] → B where B is a separable Banach space. We establish an isomorphism between Hρ(B) and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of second differences, the existence of a version in Hρ(B) for a given random field. 20...

Random Projection-Based Anderson-Darling Test for Random Fields

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...

Modeling and Estimation for a Class of Multiresolution Random Fields