Kriging for Functional Data

Abstract

Abstract Spatial functional data analysis is a relatively new topic in statistics. We have functional data when a random variable takes its values in a functional space and is observed at some sampling points. In this article, we focus on the case of functional data presenting spatial dependence, and present an overview of the existing methodology to make spatial predictions when the data values are functions. Kriging and its several related versions are widely known and used for spatial data. However, when the spatial data are functions, a bridge between functional data analysis and geostatistics has to be built. Ordinary kriging as well as cokriging and multivariate spatial prediction adapted to the case where the observations at each sampling location consist of samples of random functions are reviewed and compared.