A Kernel Indicator Variogram and Its Application to Groundwater Pollution Data
Raquel Menezes1, Pilar Garcia-Soidán2
1Mathematics and Applications, University of Minho, Portugal; 2Statistics and Operations Research, University of Vigo, Spain

Estimation of the distribution function of a spatial random process can be addressed in a parametric way, by imposing a shape or analytical expression for the distribution function. However, the data provided do not always support the distribution model assumption. An additional option is to proceed through the indicator kriging approach, which demands estimation of the indicator variogram (or the indicator covariance function). In this talk, we will present a kernel-type estimator for the latter aim, as a nonparametric alternative to the Matheron's estimator, typically used in this setting. In addition, we will check that approximation of the sill of the kernel indicator variogram provides another mechanism for estimation of the distribution function.

Numerical studies for simulated data are developed to illustrate the performance of the different approaches described for approximation of the distribution at a specific threshold. Furthermore, we will present an application of proposed techniques to a real environmental data set, where the presence of nitrate in groundwater in Beja district (Portugal) is measured. With these data, we have estimated the pollution risk, in terms of the probability that the nitrate concentration does not exceed the maximum value admitted for human consumption, allowing us to build risk maps of the referred region.

Keywords: Distribution function; Kernel method; Risk map; Structural analysis

Biography: Raquel Menezes is a lecturer and researcher in the Department of Mathematics and Applications of Minho University (Portugal). Her main interest areas are Spatial Statistics, mainly Geostatistics, and non-parametric estimation, motivated by environmental and health applications.