Object oriented spatial statistics for georeferenced tensor data

We address the problem of analysing a spatial dataset of manifold-valued observations. We propose to model the data by using a local approximation of the Riemannian manifold through a Hilbert space, where linear geostatistical methods can be developed. We discuss estimation methods for the proposed model, and consistently develop a Kriging technique for tensor data. The methodological developments are illustrated through the analysis of a real dataset dealing with covariance between temperatures and precipitation in the Quebec region of Canada