Geostatistical Functional Data Analysis

Herausgegeben:Mateu, Jorge

• Gebundenes Buch

Produktbeschreibung

Geostatistical Functional Data Analysis

Explore the intersection between geostatistics and functional data analysis with this insightful new reference

Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together 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. This book provides a complete and 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.

Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes:
_ A thorough introduction to the spatial kriging methodology when working with functions
_ A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations
_ Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region
_ In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis

Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.

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Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley / Wiley & Sons
• Artikelnr. des Verlages: 1W119387840
• 1. Auflage
• Seitenzahl: 448
• Erscheinungstermin: 13. Dezember 2021
• Englisch
• Abmessung: 226mm x 152mm x 33mm
• Gewicht: 776g
• ISBN-13: 9781119387848
• ISBN-10: 1119387841
• Artikelnr.: 60094637

Autorenporträt

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.

Inhaltsangabe

List of Contributors xiii

Foreword xvi

1 Introduction to Geostatistical Functional Data Analysis 1
Jorge Mateu and Ramón Giraldo

1.1 Spatial Statistics 1

1.2 Spatial Geostatistics 7

1.2.1 Regionalized Variables 7

1.2.2 Random Functions 7

1.2.3 Stationarity and Intrinsic Hypothesis 9

1.3 Spatiotemporal Geostatistics 12

1.3.1 Relevant Spatiotemporal Concepts 12

1.3.2 Spatiotemporal Kriging 16

1.3.3 Spatiotemporal Covariance Models 17

1.4 Functional Data Analysis in Brief 18

References 22

Part I Mathematical and Statistical Foundations 27

2 Mathematical Foundations of Functional Kriging in Hilbert Spaces and Riemannian Manifolds 29
Alessandra Menafoglio, Davide Pigoli, and Piercesare Secchi

2.1 Introduction 29

2.2 Definitions and Assumptions 30

2.3 Kriging Prediction in Hilbert Space: A Trace Approach 33

2.3.1 Ordinary and Universal Kriging in Hilbert Spaces 33

2.3.2 Estimating the Drift 36

2.3.3 An Example: Trace-Variogram in Sobolev Spaces 37

2.3.4 An Application to Nonstationary Prediction of Temperatures Profiles 39

2.4 An Operatorial Viewpoint to Kriging 42

2.5 Kriging for Manifold-Valued Random Fields 45

2.5.1 Residual Kriging 45

2.5.2 An Application to Positive Definite Matrices 47

2.5.3 Validity of the Local Tangent Space Approximation 49

2.6 Conclusion and Further Research 53

References 53

3 Universal, Residual, and External Drift Functional Kriging 55
Maria Franco-Villoria and Rosaria Ignaccolo

3.1 Introduction 56

3.2 Universal Kriging for Functional Data (UKFD) 56

3.3 Residual Kriging for Functional Data (ResKFD) 58

3.4 Functional Kriging with External Drift (FKED) 60

3.5 Accounting for Spatial Dependence in Drift Estimation 61

3.5.1 Drift Selection 62

3.6 Uncertainty Evaluation 62

3.7 Implementation Details in R 64

3.7.1 Example: Air Pollution Data 64

3.8 Conclusions 69

References 71

4 Extending Functional Kriging When Data Are Multivariate Curves: Some Technical Considerations and Operational Solutions 73
David Nerini, Claude Manté, and Pascal Monestiez

4.1 Introduction 73

4.2 Principal Component Analysis for Curves 74

4.2.1 Karhunen-Loève Decomposition 74

4.2.2 Dealing with a Sample 76

4.3 Functional Kriging in a Nutshell 78

4.3.1 Solution Based on Basis Functions 79

4.3.2 Estimation of Spatial Covariances 81

4.4 An Example with the Precipitation Observations 82

4.4.1 Fitting Variogram Model 83

4.4.2 Making Prediction 83

4.5 Functional Principal Component Kriging 85

4.6 Multivariate Kriging with Functional Data 88

4.6.1 Multivariate FPCA 91

4.6.2 MFPCA Displays 93

4.6.3 Multivariate Functional Principal Component Kriging 94

4.6.4 Mixing Temperature and Precipitation Curves 96

4.7 Discussion 98

4.A Appendices 100

4.A.1 Computation of the Kriging Variance 100

References 102

5 Geostatistical Analysis in Bayes Spaces: Probability Densities and Compositional Data 104
Alessandra Menafoglio, Piercesare Secchi, and Alberto Guadagnini

5.1 Introduction and Motivations 104

5.2 Bayes Hilbert Spaces: Natural Spaces for Functional Compositions 105

5.3 A Motivating Case Study: Particle-Size Data in Heterogeneous Aquifers -Data Description 108

5.4 Kriging Station