Geostatistical Functional Data Analysis

This book presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The editors link together for the first time the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields.

Leading experts in the field, the Editors have put together a collection of chapters covering state-of-the-art methods in this area. The individual chapters combine formal statements of the results including mathematical proofs with informal and naïve statements of classical and new results.This book serves the scientific community to know what has been done so far, and to know what type of open questions need of future answers.

After an introduction and brief overview, the book includes the following: 

• A detailed exposition of the spatial kriging methodology when dealing with functions.  
• A detailed exposition of more classical statistical techniques already adapted to the functional case and now extended in the right way to handle spatial correlations. Learning ANOVA, regression, clustering methods is crucial for a correct use of the statistical methods when the spatial correlation is present among a collection of curves sampled in a region.
• A thorough guide to understanding similarities and differences between spatio-temporal data analysis and functional data analysis. The reader will be guided in terms of modelling and computational issues.

The information here allows the reader not only to fully understand kriging methods, but to use the most innovative functional methods adapted to spatially correlated functions, to deal with spatio-temporal datasets from a functional perspective, and to being able to handle massive databases from a more computational perspective. This book provides a complete an up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field.

Jorge Mateu is Full Professor of Statistics at the Department of Mathematics of University Jaume I of Castellon. His research focuses on stochastic processes with a particular interest in spatial and spatio-temporal point processes and geostatistics.

Ramón Giraldo is Full Professor of Statistics at the Department of Statistics at the Universidad Nacional de Colombia. His research focuses on non-parametric statistics, functional data analysis, and spatial and spatio-temporal geostatistics.

Preface

1. Introduction to Geostatistical Functional Data Analysis

2. Mathematical foundations of functional Kriging in Hilbert spaces and Riemannian manifolds

3. Universal, Residual and External Drift Functional Kriging

4. Extending functional kriging when data are multivariate curves : some technical considerations and
operational solutions

5. Geostatistical analysis in Bayes spaces: probability densities and compositional data

6. Spatial functional data analysis for probability density functions: compositional functional data vs
distributional data approach

7. Clustering spatial functional data

8. Nonparametric statistical analysis of spatially distributed functional data

9. A non parametric algorithm for spatially dependent functional data: Bagging Voronoi for clustering,
dimensional reduction and regression

10. Non-parametric inference for spatio-temporal data based on local null hypothesis testing for functional data

11. A penalized regression model for spatial functional data with application to the analysis of the production of waste in Venice province

12. Quasi-Maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models

13. Spatial Prediction and Optimal Sampling for Multivariate Functional Random Fields

14. Spatio-temporal Functional Data Analysis

15. A comparison of spatio-temporal and functional kriging approaches

16. From spatio-temporal smoothing to functional spatial regression: a penalized approach

Index