Geostatistical Functional Data Analysis 1st Edition by Jorge Mateu, Ramon Giraldo ISBN 9781119387848 1119387841

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ISBN 10: 1119387841
ISBN 13: 9781119387848
Author: Jorge Mateu, Ramon Giraldo

Geostatistical Functional Data Analysis 1st Edition Table of contents:

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

Part I: Mathematical and Statistical Foundations

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

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Tags: Jorge Mateu, Ramon Giraldo, Geostatistical Functional, Data Analysis