Browsing by Author "Velandia D."

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Assessing the significance of the correlation between the components of a bivariate Gaussian random field
(John Wiley and Sons Ltd, 2015) Bevilacqua M.; Vallejos R.; Velandia D.
Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the association between autocorrelated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution of the maximum likelihood estimator of a specific parametric class of bivariate covariance models. Explicit expressions for the Fisher information matrix are given for a separable and a nonseparable version of the parametric class, leading to an asymptotic test. The empirical evidence supports our proposal, and as a result, in most of the cases, the new test performs better than the modified t test even when the bivariate covariance model is misspecified or the distribution of the bivariate random field is not Gaussian. Finally, to illustrate how the proposed test works in practice, we study a real dataset concerning the relationship between arsenic and lead from a contaminated area in Utah, USA. © 2015 John Wiley & Sons, Ltd.
Composite Likelihood Inference for Multivariate Gaussian Random Fields
(Springer New York LLC, 2016) Bevilacqua M.; Alegria A.; Velandia D.; Porcu E.
In the recent years, there has been a growing interest in proposing covariance models for multivariate Gaussian random fields. Some of these covariance models are very flexible and can capture both the marginal and the cross-spatial dependence of the components of the associated multivariate Gaussian random field. However, effective estimation methods for these models are somehow unexplored. Maximum likelihood is certainly a useful tool, but it is impractical in all the circumstances where the number of observations is very large. In this work, we consider two possible approaches based on composite likelihood for multivariate covariance model estimation. We illustrate, through simulation experiments, that our methods offer a good balance between statistical efficiency and computational complexity. Asymptotic properties of the proposed estimators are assessed under increasing domain asymptotics. Finally, we apply the method for the analysis of a bivariate dataset on chlorophyll concentration and sea surface temperature in the Chilean coast. © 2016, International Biometric Society.