TY - JOUR
T1 - Covariance functions on spheres cross time
T2 - Beyond spatial isotropy and temporal stationarity
AU - Estrade, Anne
AU - Fariñas, Alessandra
AU - Porcu, Emilio
N1 - Funding Information:
We would like to acknowledge UTFSM, Chile and GDR 3477 GeoSto from French CNRS for supporting Alessandra Fariñas research visits to Paris, and FONDECYT, Chile1170290 grant given by Chilean government, which supported Emilio Porcu and Alessandra Fariñas research.
Funding Information:
We would like to acknowledge UTFSM, Chile and GDR 3477 GeoSto from French CNRS for supporting Alessandra Fariñas research visits to Paris, and FONDECYT, Chile 1170290 grant given by Chilean government, which supported Emilio Porcu and Alessandra Fariñas research.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/8
Y1 - 2019/8
N2 - Spectral representations uniquely define the covariance functions associated to random fields defined over spheres or spheres cross time. Covariance functions on spheres cross time are usually modeled under the assumptions of either spatial isotropy or axial symmetry, and the assumption of temporal stationarity. This paper goes beyond these assumptions. In particular, we consider the problem of spatially anisotropic covariance functions on spheres. The crux of our criterion is to escape from the addition theorem for spherical harmonics. We also challenge the problem of temporal nonstationarity in nonseparable space–time covariance functions, where space is the n-dimensional sphere.
AB - Spectral representations uniquely define the covariance functions associated to random fields defined over spheres or spheres cross time. Covariance functions on spheres cross time are usually modeled under the assumptions of either spatial isotropy or axial symmetry, and the assumption of temporal stationarity. This paper goes beyond these assumptions. In particular, we consider the problem of spatially anisotropic covariance functions on spheres. The crux of our criterion is to escape from the addition theorem for spherical harmonics. We also challenge the problem of temporal nonstationarity in nonseparable space–time covariance functions, where space is the n-dimensional sphere.
KW - Gegenbauer polynomial
KW - Positive definite
KW - Space–time random field
KW - Spectral representation
KW - Spherical harmonic
UR - http://www.scopus.com/inward/record.url?scp=85063643069&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2019.03.011
DO - 10.1016/j.spl.2019.03.011
M3 - Article
AN - SCOPUS:85063643069
SN - 0167-7152
VL - 151
SP - 1
EP - 7
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -