Nonparametric Estimation of Spatial and Space-Time Covariance Function

Covariance structure modeling plays a key role in the spatial data analysis. Various parametric models have been developed to accommodate the idiosyncratic features of a given dataset. However, the parametric models may impose unjustified restrictions to the covariance structure and the procedure of choosing a specific model is often ad hoc. To avoid the choice of parametric forms, we propose a nonparametric covariance estimator for the spatial data, as well as its extension to the spatio-temporal data based on the class of space-time covariance models developed by Gneiting (J. Am. Stat. Assoc. 97:590-600, 2002). Our estimator is obtained via a nonparametric approximation of completely monotone functions. It is easy to implement and our simulation shows it outperforms the parametric models when there is no clear information on model specification. Two real datasets are analyzed to illustrate our approach and provide further comparison between the nonparametric estimator and parametric models.