TY - JOUR
T1 - Unifying compactly supported and Matérn covariance functions in spatial statistics
AU - Bevilacqua, Moreno
AU - Caamaño-Carrillo, Christian
AU - Porcu, Emilio
N1 - Funding Information:
Partial support was provided by FONDECYT grant 1200068 of Chile, by regional MATH-AmSud program, Chile , Grant Number 20-MATH-03 and by ANID/PIA/ANILLOS, Chile ACT210096 for Moreno Bevilacqua, Chile , and by FONDECYT grant 11220066 of Chile, DIUBB, Chile 2120538 IF/R (University of Bío-Bío) for Christian Caamaño-Carrillo, Chile .
Publisher Copyright:
© 2022
PY - 2022/5
Y1 - 2022/5
N2 - The Matérn family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matérn case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported. More importantly, we show that the proposed covariance family generalizes the Matérn model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matérn model with an extra-parameter that allows for switching from compactly to globally supported covariance functions. Our numerical experiments elucidate the speed of convergence of the proposed model to the Matérn model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.
AB - The Matérn family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matérn case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported. More importantly, we show that the proposed covariance family generalizes the Matérn model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matérn model with an extra-parameter that allows for switching from compactly to globally supported covariance functions. Our numerical experiments elucidate the speed of convergence of the proposed model to the Matérn model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.
KW - Fixed domain asymptotics
KW - Gaussian random fields
KW - Generalized wendland model
KW - Sparse matrices
UR - http://www.scopus.com/inward/record.url?scp=85123743484&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2022.104949
DO - 10.1016/j.jmva.2022.104949
M3 - Article
AN - SCOPUS:85123743484
SN - 0047-259X
VL - 189
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104949
ER -