Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

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Object oriented spatial statistics for georeferenced tensor data
Alessandra Menafoglio, Davide Pigoli, Piercesare Secchi

Last modified: 2018-05-28

Abstract


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

References


Cressie, N. (1993). Statistics for Spatial Data. New York: John Wiley & Sons. Lee, J. (2012) Introduction to Smooth Manifolds, 218, Springer Science & Business Media.

Menafoglio, A., P. Secchi, and M. Dalla Rosa (2013). A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space. Electronic Journal of Statistics 7, 2209–2240.

Menafoglio, A. and P. Secchi (2017). Statistical analysis of complex and spatially dependent data: a review of object oriented spatial statistics. European Journal of Operational Research 258(2), 401–410.

Menafoglio, A., Gaetani, G., Secchi, P. (2018) Random domain decompositions for object-oriented kriging over complex domains, MOX-report 10/2018, Politecnico di Milano.

Pigoli, D., Menafoglio, A., Secchi, P. (2016) Kriging prediction for manifold-valued random fields. Journal of Multivariate Analysis, 145, 117–131.


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