Geostatistical Functional Data Analysis
- Length: 448 pages
- Edition: 1
- Language: English
- Publisher: Wiley
- Publication Date: 2022-01-04
- ISBN-10: 1119387841
- ISBN-13: 9781119387848
- Sales Rank: #0 (See Top 100 Books)
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.
Cover Table of Contents Title Page Copyright List of Contributors Foreword Part I: Mathematical and Statistical Foundations 1 Introduction to Geostatistical Functional Data Analysis 1.1 Spatial Statistics 1.2 Spatial Geostatistics 1.3 Spatiotemporal Geostatistics 1.4 Functional Data Analysis in Brief References 2 Mathematical Foundations of Functional Kriging in Hilbert Spaces and Riemannian Manifolds 2.1 Introduction 2.2 Definitions and Assumptions 2.3 Kriging Prediction in Hilbert Space: A Trace Approach 2.4 An Operatorial Viewpoint to Kriging 2.5 Kriging for Manifold-Valued Random Fields 2.6 Conclusion and Further Research References 3 Universal, Residual, and External Drift Functional Kriging 3.1 Introduction 3.2 Universal Kriging for Functional Data (UKFD) 3.3 Residual Kriging for Functional Data (ResKFD) 3.4 Functional Kriging with External Drift (FKED) 3.5 Accounting for Spatial Dependence in Drift Estimation 3.6 Uncertainty Evaluation 3.7 Implementation Details in R 3.8 Conclusions References 4 Extending Functional Kriging When Data Are Multivariate Curves: Some Technical Considerations and Operational Solutions 4.1 Introduction 4.2 Principal Component Analysis for Curves 4.3 Functional Kriging in a Nutshell 4.4 An Example with the Precipitation Observations 4.5 Functional Principal Component Kriging 4.6 Multivariate Kriging with Functional Data 4.7 Discussion 4.A Appendices References 5 Geostatistical Analysis in Bayes Spaces: Probability Densities and Compositional Data 5.1 Introduction and Motivations 5.2 Bayes Hilbert Spaces: Natural Spaces for Functional Compositions 5.3 A Motivating Case Study: Particle-Size Data in Heterogeneous Aquifers – Data Description 5.4 Kriging Stationary Functional Compositions 5.5 Analyzing Nonstationary Fields of FCs 5.6 Conclusions and Perspectives References 6 Spatial Functional Data Analysis for Probability Density Functions: Compositional Functional Data vs. Distributional Data Approach 6.1 FDA and SDA When Data Are Densities 6.2 Measures of Spatial Association for Georeferenced Density Functions 6.3 Real Data Analysis 6.4 Conclusion Acknowledgments References Notes Part II: Statistical Techniques for Spatially Correlated Functional Data 7 Clustering Spatial Functional Data 7.1 Introduction 7.2 Model-Based Clustering for Spatial Functional Data 7.3 Descendant Hierarchical Classification (HC) Based on Centrality Methods 7.4 Application 7.5 Conclusion References 8 Nonparametric Statistical Analysis of Spatially Distributed Functional Data 8.1 Introduction 8.2 Large Sample Properties 8.3 Prediction 8.4 Numerical Results 8.5 Conclusion 8 Appendix References 9 A Nonparametric Algorithm for Spatially Dependent Functional Data: Bagging Voronoi for Clustering, Dimensional Reduction, and Regression 9.1 Introduction 9.2 The Motivating Application 9.3 The Bagging Voronoi Strategy 9.4 Bagging Voronoi Clustering (BVClu) 9.5 Bagging Voronoi Dimensional Reduction (BVDim) 9.6 Bagging Voronoi Regression (BVReg) 9.7 Conclusions and Discussion References Note 10 Nonparametric Inference for Spatiotemporal Data Based on Local Null Hypothesis Testing for Functional Data 10.1 Introduction 10.2 Methodology 10.3 Data Analysis 10.4 Conclusion and Future Works References 11 Modeling Spatially Dependent Functional Data by Spatial Regression with Differential Regularization 11.1 Introduction 11.2 Spatial Regression with Differential Regularization for Geostatistical Functional Data 11.3 Simulation Studies 11.4 An Illustrative Example: Study of the Waste Production in Venice Province 11.5 Model Extensions References Notes 12 Quasi-maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models 12.1 Introduction 12.2 Model 12.3 Results and Assumptions 12.4 Numerical Experiments 12.5 Conclusion 12.A Appendix References 13 Spatial Prediction and Optimal Sampling for Multivariate Functional Random Fields 13.1 Background 13.2 Functional Kriging 13.3 Functional Cokriging 13.4 Optimal Sampling Designs for Spatial Prediction of Functional Data 13.5 Real Data Analysis 13.6 Discussion and Conclusions References Part III: Spatio–Temporal Functional Data 14 Spatio–temporal Functional Data Analysis 14.1 Introduction 14.2 Randomness Test 14.3 Change-Point Test 14.4 Separability Tests 14.5 Trend Tests 14.6 Spatio–Temporal Extremes References 15 A Comparison of Spatiotemporal and Functional Kriging Approaches 15.1 Introduction 15.2 Preliminaries 15.3 Kriging 15.4 A Simulation Study 15.5 Application: Spatial Prediction of Temperature Curves in the Maritime Provinces of Canada 15.6 Concluding Remarks References 16 From Spatiotemporal Smoothing to Functional Spatial Regression: a Penalized Approach 16.1 Introduction 16.2 Smoothing Spatial Data via Penalized Regression 16.3 Penalized Smooth Mixed Models 16.4 P-spline Smooth ANOVA Models for Spatial and Spatiotemporal data 16.5 P-spline Functional Spatial Regression 16.6 Application to Air Pollution Data Acknowledgments References Index End User License Agreement
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