Study of spatial relationships between two sets of variables: a nonparametric approach

We propose a new method for estimating a codispersion coefficient to quantify the association between two spatial variables. Our proposal is based on a Nadaraya-Watson version of the codispersion coefficient through a suitable kernel. Under regularity conditions, we derive expressions for the bias and mean square error for a kernel version of the cross-variogram and establish the consistency of a Nadaraya-Watson estimator of the codispersion coefficient. In addition, we propose a bandwidth selection method for both the variogram and the cross-variogram. Monte Carlo simulations support the theoretical findings, and as a result, the new proposal performs better than the classic Matheron's estimator. The proposed method is useful for quantifying spatial associations between two variables measured at the same location. Finally, we study forest data concerning the relationship among the tree height, basal area, elevation and slope of Pinus radiata plantations. A two-dimensional codispersion map is constructed to provide insight into the spatial association between these variables.