Testing the covariance structure of multivariate random fields

Bo Li, Marc G. Genton, Michael Sherman

Research output: Contribution to journalArticle

Abstract

There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.

Original languageEnglish (US)
Pages (from-to)813-829
Number of pages17
JournalBiometrika
Volume95
Issue number4
DOIs
StatePublished - Dec 1 2008
Externally publishedYes

Fingerprint

Covariance Structure
Random Field
Covariance Function
Describing functions
Testing
Methodology
Coregionalization
Power of Test
Trivariate
Spatio-temporal Data
Temporal Correlation
Multivariate Functions
Evaluate
testing
Multivariate Data
Spatial Correlation
Separability
Pollutants
Normality
Simulation Experiment

Keywords

  • Covariance
  • Linear model of coregionalization
  • Separability
  • Space and time
  • Symmetry

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Testing the covariance structure of multivariate random fields. / Li, Bo; Genton, Marc G.; Sherman, Michael.

In: Biometrika, Vol. 95, No. 4, 01.12.2008, p. 813-829.

Research output: Contribution to journalArticle

Li, Bo ; Genton, Marc G. ; Sherman, Michael. / Testing the covariance structure of multivariate random fields. In: Biometrika. 2008 ; Vol. 95, No. 4. pp. 813-829.
@article{25dc16ca9797481db975f20812e06942,
title = "Testing the covariance structure of multivariate random fields",
abstract = "There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.",
keywords = "Covariance, Linear model of coregionalization, Separability, Space and time, Symmetry",
author = "Bo Li and Genton, {Marc G.} and Michael Sherman",
year = "2008",
month = "12",
day = "1",
doi = "10.1093/biomet/asn053",
language = "English (US)",
volume = "95",
pages = "813--829",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "4",

}

TY - JOUR

T1 - Testing the covariance structure of multivariate random fields

AU - Li, Bo

AU - Genton, Marc G.

AU - Sherman, Michael

PY - 2008/12/1

Y1 - 2008/12/1

N2 - There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.

AB - There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.

KW - Covariance

KW - Linear model of coregionalization

KW - Separability

KW - Space and time

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=57249090982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57249090982&partnerID=8YFLogxK

U2 - 10.1093/biomet/asn053

DO - 10.1093/biomet/asn053

M3 - Article

AN - SCOPUS:57249090982

VL - 95

SP - 813

EP - 829

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 4

ER -