The characterization problem for isotropic covariance functions

被引:18
作者
Gneiting, T
Sasvári, Z
机构
[1] Univ Washington, Dept Stat, Seattle, WA 98195 USA
[2] Tech Univ Dresden, Dept Math, D-01062 Dresden, Germany
来源
MATHEMATICAL GEOLOGY | 1999年 / 31卷 / 01期
关键词
correlation function; extension theorem; nugget effect; positive definite; radial; Schoenberg's conjecture;
D O I
10.1023/A:1007597415185
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
Isotropic covariance functions are successfully used to model spatial continuity in a multitude of scientific disciplines. Nevertheless, a satisfactory characterization of the class of permissible isotropic covariance models has been missing. The intention of this note is to review, complete, and extend the existing literature on the problem. As it turns out, a famous conjecture of Schoenberg (1938) holds true: any measurable, isotropic covariance function on R-d (d greater than or equal to 2) admits a decomposition as the sum of a pure nugget effect and a continuous covariance function. Moreover any measurable, isotropic covariance function defined on a ball in R-d can be extended to an isotropic covariance function defined on the entire space R-d.
引用
收藏
页码:105 / 111
页数:7
相关论文
共 21 条
[1]   TESTING VARIOGRAMS FOR POSITIVE-DEFINITENESS [J].
ARMSTRONG, M ;
DIAMOND, P .
JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR MATHEMATICAL GEOLOGY, 1984, 16 (04) :407-421
[2]   ON THE THEORY OF ELLIPTICALLY CONTOURED DISTRIBUTIONS [J].
CAMBANIS, S ;
HUANG, S ;
SIMONS, G .
JOURNAL OF MULTIVARIATE ANALYSIS, 1981, 11 (03) :368-385
[3]   ON THE PROBLEM OF PERMISSIBLE COVARIANCE AND VARIOGRAM MODELS [J].
CHRISTAKOS, G .
WATER RESOURCES RESEARCH, 1984, 20 (02) :251-265
[4]  
Christakos G., 1992, Random field models in earth sciences
[5]  
Cressie N., 1993, STAT SPATIAL DATA
[6]  
Crum M. M., 1956, P LONDON MATH SOC 3, Vs3-6, P548, DOI [10.1112/plms/s3-6.4.548, DOI 10.1112/PLMS/S3-6.4.548]
[7]   TWO-DIMENSIONAL MARKOV SPECTRUM ESTIMATES NEED NOT EXIST [J].
DICKINSON, BW .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1980, 26 (01) :120-121
[8]  
GNEITING T, 1998, IN PRESS MATH NACHR
[9]  
GNEITING T, 1998, IN PRESS ADV APPL PR
[10]  
GUTTORP P, 1994, J AM STAT ASSOC, V89, P382