Modified half-region depth for spatially dependent functional data

In this paper, we address the problem of getting order statistics for georeferenced functional data by means of depth functions. To reach this aim, we introduce the concept of spatial dispersion function for functional data in a specific location of the geographic space. Then we generalize the notion of modified half-region depth to spatial dispersion functions. Through the use of spatial dispersion functions we show how the data ordering criterion depends not only on the functional but also on the spatial component. The proposal is applied to two wide simulation studies and to real data coming from sensors.