Variograms: Taboos, Conjectures and Facts

In this seminar we show results that may be of interest for the mathematic and spatial statistics community as well.
We show that a large subclass of variograms is closed under Schur products and that some desirable stability properties,
like the Schur product of ad hoc compositions, can be obtained under the proposed setting. We
introduce new classes of kernels of Schoenberg-L´evy type and show some important
properties of eventually constant, radially symmetric variograms. In particular,
we characterize eventually constant variograms in terms of their permissibility in
Euclidean spaces of arbitrary high dimension. All the results are discussed in the
light of implications for spatial statisticians.