A depth function for geostatistical functional data

Abstract

In this paper we introduce a depth measure for geostatistical functional data. The aim is to provide a tool which allows to get a center-outward ordering of functional data recorded by sensors placed on a geographic area. Although the topic of ordering functional data has already been addressed in the literature, no proposal analyzes the case in which there is a spatial dependence among the curves. With this aim, we extend a well-known depth measure for functional data by introducing a new component in the measurement, which accounts for the spatial covariance. An application of the proposed method to a wide range of simulated cases shows its effectiveness in discovering a useful ordering of the spatially located curves.