Admissible nested covariance models over spheres cross time

Author(s)

Peron, Ana ^[1] ; Porcu, Emilio ^{[2, 3]} ; Emery, Xavier ^{[4, 5]}

Affiliation

^[1] Univ Sao Paulo, ICMC, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Newcastle, Sch Math & Stat, Newcastle Upon Tyne, Tyne & Wear - England

^[3] Univ Atacama, Dept Math, Copiapo - Chile

^[4] Univ Chile, Dept Min Engn, Santiago - Chile

^[5] Univ Chile, Adv Min Technol Ctr, Santiago - Chile

• Document type: Journal article
• Source: STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT; v. 32, n. 11, p. 3053-3066, NOV 2018.
• Web of Science Citations: 2

Abstract

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. (AU)

• FAPESP's process: 16/03015-7 - Positive definite functions
• Grantee: Ana Paula Peron
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
• Grantee: Dimitar Kolev Dimitrov
• Support Opportunities: Research Projects - Thematic Grants