@article{d3dd479c4fc648aa8002e37258057469,
title = "Contours and dimple for the Gneiting class of space-time correlation functions",
abstract = "We offer a dual view of the dimple problem related to space-time correlation functions in terms of their contours.We find that the dimple property (Kent et al., 2011) in the Gneiting class of correlations is in oneto-one correspondence with nonmonotonicity of the parametric curve describing the associated contour lines. Further, we show that given such a nonmonotonic parametric curve associated with a given level set, all the other parametric curves at smaller levels inherit the nonmonotonicity. We propose a modified Gneiting class of correlations having monotonically decreasing parametric curves and no dimple along the temporal axis.",
keywords = "Dimple, Gneiting correlation function, Isoline, Random field",
author = "F. Cuevas and E. Porcu and M. Bevilacqua",
note = "Funding Information: We are grateful to two referees and the associate editor for comments that have helped to improve the manuscript. The first author was supported by the Danish Council for Independent Research – Natural Sciences, and by the Centre for Stochastic Geometry and Advanced Bioimaging, from the Villum Foundation. The second and third authors were partially supported by Fondecyt from the Ministry of Education, Chile. This research project began when the second author was affiliated with the University Federico Santa Mar{\'i}a. Publisher Copyright: {\textcopyright} 2017 Biometrika Trust.",
year = "2017",
month = dec,
day = "1",
doi = "10.1093/biomet/asx048",
language = "English",
volume = "104",
pages = "995--1001",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "4",
}