On some matérn covariance functions for spatio-temporal random fields

Ryan H. L. IP, Wai Keung LI

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The Matérn class is an important class of covariance functions in spatial statistics. With the recent flourishing trend in modelling spatio-temporal data, indepth theoretical development of spatio-temporal covariograms is needed. In this paper, theories under the infill asymptotic framework concerning estimation issues of a generally non-separable Matérn class of spatio-temporal covariance function is presented. It is found that not all parameters can be estimated consistently while quantities that can be estimated consistently are found based on equivalence and orthogonality of Gaussian measures. The micro-ergodic parameters are found to be different when the degrees of separability between the space and time components are different. For the computation, an easy-to-implement estimation procedure is given. Simulation studies are conducted to show how well the asymptotic results apply when the sample size is moderate. A set of air pollution data is used to demonstrate the usefulness of the estimation procedure suggested. Copyright © 2017 Institute of Statistical Science.
Original languageEnglish
Pages (from-to)805-822
JournalStatistica Sinica
Volume27
DOIs
Publication statusPublished - Apr 2017

Fingerprint

Covariance Function
Random Field
Infill Asymptotics
Spatial Statistics
Spatio-temporal Data
Gaussian Measure
Air Pollution
Nonseparable
Separability
Orthogonality
Sample Size
Equivalence
Simulation Study
Modeling
Demonstrate
Class
Random field

Citation

Ip, R. H. L., & Li, W. K. (2017). On some matérn covariance functions for spatio-temporal random fields. Statistica Sinica, 27, 805-822. doi: 10.5705/ss.202015.0037

Keywords

  • Gaussian measures
  • Infill asymptotics
  • Micro-ergodic parameters
  • Space-time data