Admissible nested covariance models over spheres cross time

Ana Peron, Emilio Porcu, Xavier Emery

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Nested covariance models, defined as linear combinations of basic covariance functions, are very popular in many branches of applied statistics, and in particular in geostatistics. A notorious limit of nested models is that the constants in the linear combination are bound to be nonnegative in order to preserve positive definiteness (admissibility). This paper studies nested models on d-dimensional spheres and spheres cross time. We show the exact interval of admissibility for the constants involved in the linear combinations. In particular, we show that at least one constant can be negative. One of the implications is that one can obtain a nested model attaining negative correlations. We provide characterization theorems for arbitrary linear combinations as well as for nonconvex combinations involving two covariance functions. We illustrate our findings through several examples involving nonconvex combinations of well-known parametric families of covariance functions.

Original languageBritish English
Pages (from-to)3053-3066
Number of pages14
JournalStochastic Environmental Research and Risk Assessment
Issue number11
StatePublished - 1 Nov 2018


  • Covariance functions
  • Negative covariance
  • Nested models
  • Spheres


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