Kelly, Gabrielle E.Gabrielle E.KellyMenezes, RaquelRaquelMenezes2019-05-272019-05-272018 ECOST2018-12-16978-9963-2227-5-9http://hdl.handle.net/10197/10672The 12th International Conference on Computational and Financial Econometrics (CFE 2018) and the 11th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computational and Methodological Statistics (CMStatistics 2018), Pisa, Italy, 14-16 December 2018Estimation of the variogram and associated parameters in spatial analysis is important for assessing spatial dependence and in predicting values of the measured variable at unsampled locations i.e. kriging. A simulation study is implemented to compare the performance of (i) Gaussian restricted maximum likelihood (REML) estimation, (ii) curve-fitting by ordinary least squares and (iii) nonparametric Shapiro-Botha estimation for estimating the covariance structure of a stationary Gaussian spatial process and a spatial process with t-distributed margins. Processes with Matern covariance functions are considered and the parameters estimated are the nugget, partial sill and practical range. Both parametric and nonparametric bootstrap distributions of the estimators are computed and compared to the true marginal distributions of the estimators. Gaussian REML is the estimator of choice for both Gaussian and t-distributed data and all choices of Matern variogram. However, accurate estimation of the Matern shape parameter is critical to achieving a good fit while this does not affect the Shapiro-Botha estimator. The parametric and nonparametric bootstrap both performed well, the latter being better for the Shapiro-Botha estimates. A numerical example, obtained from environmental monitoring, is included to illustrate the application of the methods and the bootstrap.enSpatial analysisGaussian restricted maximum likelihood (REML)Shapiro-Botha estimatesBootstrapConference Publication85852018-12-17https://creativecommons.org/licenses/by-nc-nd/3.0/ie/