TY - JOUR
T1 - Composite likelihood estimation for a Gaussian process under fixed domain asymptotics
AU - Bachoc, François
AU - Bevilacqua, Moreno
AU - Velandia, D.
N1 - Funding Information:
The research work conducted by Moreno Bevilacqua was supported in part by FONDECYT, Chile grant 1160280 , Chile and by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, Chile , grant ”Millennium Nucleus Center for the Discovery of Structures in Complex Data”.
Funding Information:
The research work conducted by Moreno Bevilacqua was supported in part by FONDECYT, Chile grant 1160280, Chile and by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, Chile, grant ?Millennium Nucleus Center for the Discovery of Structures in Complex Data?. We thank the editor in chief, the associate editor and two anonymous referees for their constructive feedback and helpful suggestions.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/11
Y1 - 2019/11
N2 - We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the microergodic parameter can be consistent or inconsistent. This depends on the range of admissible parameter values in the likelihood optimization. On the other hand, the weighted pairwise conditional maximum likelihood estimator is always consistent. Both estimators are also asymptotically Gaussian when they are consistent. Their asymptotic variances are larger or strictly larger than that of the maximum likelihood estimator. A simulation study is presented in order to compare the finite sample behavior of the pairwise likelihood estimators with their asymptotic distributions. For more general covariance functions, an additional inconsistency result is provided, for the weighted pairwise maximum likelihood estimator of a variance parameter.
AB - We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the microergodic parameter can be consistent or inconsistent. This depends on the range of admissible parameter values in the likelihood optimization. On the other hand, the weighted pairwise conditional maximum likelihood estimator is always consistent. Both estimators are also asymptotically Gaussian when they are consistent. Their asymptotic variances are larger or strictly larger than that of the maximum likelihood estimator. A simulation study is presented in order to compare the finite sample behavior of the pairwise likelihood estimators with their asymptotic distributions. For more general covariance functions, an additional inconsistency result is provided, for the weighted pairwise maximum likelihood estimator of a variance parameter.
KW - Asymptotic normality
KW - Consistency
KW - Exponential model
KW - Fixed-domain asymptotics
KW - Gaussian processes
KW - Large data sets
KW - Microergodic parameters
KW - Pairwise composite likelihood
UR - http://www.scopus.com/inward/record.url?scp=85069691334&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2019.104534
DO - 10.1016/j.jmva.2019.104534
M3 - Article
AN - SCOPUS:85069691334
VL - 174
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
M1 - 104534
ER -