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Geostatistical Functional Data Analysis [Kõva köide]

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  • Formaat: Hardback, 448 pages, kõrgus x laius x paksus: 221x150x31 mm, kaal: 794 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 09-Dec-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119387841
  • ISBN-13: 9781119387848
Teised raamatud teemal:
Geostatistical Functional Data AnalysisSuurem pilt
  • Formaat: Hardback, 448 pages, kõrgus x laius x paksus: 221x150x31 mm, kaal: 794 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 09-Dec-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119387841
  • ISBN-13: 9781119387848
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781119387848.html
Märksõnad:

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.

List of Contributors
xiii
Foreword xvi
1 Introduction to Geostatistical Functional Data Analysis
1(26)
Jorge Mateu
Ramdn Giratdo
1.1 Spatial Statistics
1(6)
1.2 Spatial Geostatistics
7(5)
1.2.1 Regionalized Variables
7(1)
1.2.2 Random Functions
7(2)
1.2.3 Stationarity and Intrinsic Hypothesis
9(3)
1.3 Spatiotemporal Geostatistics
12(6)
1.3.1 Relevant Spatiotemporal Concepts
12(4)
1.3.2 Spatiotemporal Kriging
16(1)
1.3.3 Spatiotemporal Covariance Models
17(1)
1.4 Functional Data Analysis in Brief
18(9)
References
22(5)
Part I Mathematical and Statistical Foundations
27(128)
2 Mathematical Foundations of Functional Kriging in Hilbert Spaces and Riemannian Manifolds
29(26)
Alessandra Menafoglio
Davide Pigoti
Piercesare Secchi
2.1 Introduction
29(1)
2.2 Definitions and Assumptions
30(3)
2.3 Kriging Prediction in Hilbert Space: A Trace Approach
33(9)
2.3.1 Ordinary and Universal Kriging in Hilbert Spaces
33(3)
2.3.2 Estimating the Drift
36(1)
2.3.3 An Example: Trace-Variogram in Sobolev Spaces
37(2)
2.3.4 An Application to Nonstationary Prediction of Temperatures Profiles
39(3)
2.4 An Operatorial Viewpoint to Kriging
42(3)
2.5 Kriging for Manifold-Valued Random Fields
45(8)
2.5.1 Residual Kriging
45(2)
2.5.2 An Application to Positive Definite Matrices
47(2)
2.5.3 Validity of the Local Tangent Space Approximation
49(4)
2.6 Conclusion and Further Research
53(2)
References
53(2)
3 Universal, Residual, and External Drift Functional Kriging
55(18)
Maria Franco-Villoria
Rosaria Ignaccolo
3.1 Introduction
56(1)
3.2 Universal Kriging for Functional Data (UKFD)
56(2)
3.3 Residual Kriging for Functional Data (ResKFD)
58(2)
3.4 Functional Kriging with External Drift (FKED)
60(1)
3.5 Accounting for Spatial Dependence in Drift Estimation
61(1)
3.5.1 Drift Selection
62(1)
3.6 Uncertainty Evaluation
62(2)
3.7 Implementation Details in R
64(5)
3.7.1 Example: Air Pollution Data
64(5)
3.8 Conclusions
69(4)
References
71(2)
4 Extending Functional Kriging When Data Are Multivariate Curves: Some Technical Considerations and Operational Solutions
73(31)
David Nerini
Claude Mante
Pascal Monestiez
4.1 Introduction
73(1)
4.2 Principal Component Analysis for Curves
74(4)
4.2.1 Karhunen--Loeve Decomposition
74(2)
4.2.2 Dealing with a Sample
76(2)
4.3 Functional Kriging in a Nutshell
78(4)
4.3.1 Solution Based on Basis Functions
79(2)
4.3.2 Estimation of Spatial Covariances
81(1)
4.4 An Example with the Precipitation Observations
82(3)
4.4.1 Fitting Variogram Model
83(1)
4.4.2 Making Prediction
83(2)
4.5 Functional Principal Component Kriging
85(3)
4.6 Multivariate Kriging with Functional Data
88(10)
4.6.1 Multivariate FPCA
91(2)
4.6.2 MFPCA Displays
93(1)
4.6.3 Multivariate Functional Principal Component Kriging
94(2)
4.6.4 Mixing Temperature and Precipitation Curves
96(2)
4.7 Discussion
98(6)
4.A Appendices
100(1)
4.A.1 Computation of the Kriging Variance
100(2)
References
102(2)
5 Geostatistical Analysis in Bayes Spaces: Probability Densities and Compositional Data
104(24)
Alessandra Menafoglio
Piercesare Secchi
Alberto Guadagnini
5.1 Introduction and Motivations
104(1)
5.2 Bayes Hilbert Spaces: Natural Spaces for Functional Compositions
105(3)
5.3 A Motivating Case Study: Particle-Size Data in Heterogeneous Aquifers - Data Description
108(2)
5.4 Kriging Stationary Functional Compositions
110(9)
5.4.1 Model Description
110(2)
5.4.2 Data Preprocessing
112(1)
5.4.3 An Example of Application
113(3)
5.4.4 Uncertainty Assessment
116(3)
5.5 Analyzing Nonstationary Fields of FCs
119(4)
5.6 Conclusions and Perspectives
123(5)
References
124(4)
6 Spatial Functional Data Analysis for Probability Density Functions: Compositional Functional Data vs. Distributional Data Approach
128(27)
Elvira Romano
Antonio Irpino
Jorge Mateu
6.1 FDA and SDA When Data Are Densities
130(8)
6.1.1 Features of Density Functions as Compositional Functional Data
131(4)
6.1.2 Features of Density Functions as Distributional Data
135(3)
6.2 Measures of Spatial Association for Georeferenced Density Functions
138(3)
6.2.1 Identification of Spatial Clusters by Spatial Association Measures for Density Functions
139(2)
6.3 Real Data Analysis
141(8)
6.3.1 The SDA Distributional Approach
143(2)
6.3.2 The Compositional-Functional Approach
145(2)
6.3.3 Discussion
147(2)
6.4 Conclusion
149(6)
Acknowledgments
151(1)
References
151(4)
Part II Statistical Techniques for Spatially Correlated Functional Data
155(196)
7 Clustering Spatial Functional Data
157(18)
Vincent Vandewalle
Cristian Preda
Sophie Dabo-Niang
7.1 Introduction
157(1)
7.2 Model-Based Clustering for Spatial Functional Data
158(4)
7.2.1 The Expectation--Maximization (EM) Algorithm
160(1)
7.2.1.1 E Step
161(1)
7.2.1.2 M Step
161(1)
7.2.2 Model Selection
161(1)
7.3 Descendant Hierarchical Classification (HC) Based on Centrality Methods
162(3)
7.3.1 Methodology
164(1)
7.4 Application
165(6)
7.4.1 Model-Based Clustering
167(2)
7.4.2 Hierarchical Classification
169(2)
7.5 Conclusion
171(4)
References
172(3)
8 Nonparametric Statistical Analysis of Spatially Distributed Functional Data
175(36)
Sophie Dabo-Niang
Camille Ternynck
Baba Thiam
Anne-Frangoise Yao
8.1 Introduction
175(3)
8.2 Large Sample Properties
178(3)
8.2.1 Uniform Almost Complete Convergence
180(1)
8.3 Prediction
181(3)
8.4 Numerical Results
184(9)
8.4.1 Bandwidth Selection Procedure
184(1)
8.4.2 Simulation Study
185(8)
8.5 Conclusion
193(18)
8.A Appendix
194(1)
8.A.1 Some Preliminary Results for the Proofs
194(2)
8.A.2 Proofs
196(1)
8.A.2.1 Proof of Theorem 8.1
196(1)
8.A.2.2 Proof of Lemma A.3
196(1)
8.A.2.3 Proof of Lemma A.4
196(5)
8.A.2.4 Proof of Lemma A.5
201(1)
8A.2.5 Proof of Lemma A.6
201(1)
8A.2.6 Proof of Theorem 8.2
202(5)
References
207(4)
9 A Nonparametric Algorithm for Spatially Dependent Functional Data: Bagging Voronoi for Clustering, Dimensional Reduction, and Regression
211(31)
Valeria Vitelli
Federica Passamonti
Simone Vantini
Piercesare Secchi
9.1 Introduction
211(1)
9.2 The Motivating Application
212(4)
9.2.1 Data Preprocessing
214(2)
9.3 The Bagging Voronoi Strategy
216(2)
9.4 Bagging Voronoi Clustering (BVClu)
218(5)
9.4.1 BVClu of the Telecom Data
221(1)
9.4.1.1 Setting the BVClu Parameters
221(2)
9.4.1.2 Results
223(1)
9.5 Bagging Voronoi Dimensional Reduction (BVDim)
223(8)
9.5.1 BVDim of the Telecom Data
225(1)
9.5.1.1 Setting the BVDim Parameters
225(2)
9.5.1.2 Results
227(4)
9.6 Bagging Voronoi Regression (BVReg)
231(5)
9.6.1 Covariate Information: The DUSAF Data
232(2)
9.6.2 BVReg of the Telecom Data
234(1)
9.6.2.1 Setting the BVReg Parameters
234(1)
9.6.2.2 Results
235(1)
9.7 Conclusions and Discussion
236(6)
References
239(3)
10 Nonparametric Inference for Spatiotemporal Data Based on Local Null Hypothesis Testing for Functional Data
242(18)
Atessia Pini
Simone Vantini
10.1 Introduction
242(2)
10.2 Methodology
244(6)
10.2.1 Comparing Means of Two Functional Populations
244(4)
10.2.2 Extensions
248(1)
10.2.2.1 Multiway FANOVA
249(1)
10.3 Data Analysis
250(6)
10.4 Conclusion and Future Works
256(4)
References
258(2)
11 Modeling Spatially Dependent Functional Data by Spatial Regression with Differential Regularization
260(26)
Mara S. Bernardi
Laura M. Sangalli
11.1 Introduction
260(4)
11.2 Spatial Regression with Differential Regularization for Geostatistical Functional Data
264(10)
11.2.1 A Separable Spatiotemporal Basis System
265(3)
11.2.2 Discretization of the Penalized Sum-of-Square Error Functional
268(3)
11.2.3 Properties of the Estimators
271(2)
11.2.4 Model Without Covariates
273(1)
11.2.5 An Alternative Formulation of the Model
274(1)
11.3 Simulation Studies
274(4)
11.4 An Illustrative Example: Study of the Waste Production in Venice Province
278(4)
11.4.1 The Venice Waste Dataset
278(1)
11.4.2 Analysis of Venice Waste Data by Spatial Regression with Differential Regularization
279(3)
11.5 Model Extensions
282(4)
References
283(3)
12 Quasi-maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models
286(43)
Mohamed-Salem Ahmed
Laurence Broze
Sophie Dabo-Niang
Zied Gharbi
12.1 Introduction
286(2)
12.2 Model
288(5)
12.2.1 Truncated Conditional Likelihood Method
291(2)
12.3 Results and Assumptions
293(5)
12.4 Numerical Experiments
298(14)
12.4.1 Monte Carlo Simulations
298(7)
12.4.2 Real Data Application
305(7)
12.5 Conclusion
312(17)
12.A Appendix
313(1)
Proof of Proposition 12.A.1
313(1)
Proof of Theorem 12.1
314(3)
Proof of Theorem 12.2
317(2)
Proof of Theorem 12.3
319(3)
Proof of Lemma 12.A.2
322(1)
Proof of Lemma 12.A.3
322(1)
Proof of Lemma 12.A.5
323(2)
References
325(4)
13 Spatial Prediction and Optimal Sampling for Multivariate Functional Random Fields
329(22)
Martha Bohorquez
Ramon Giraldo
Jorge Mateu
13.1 Background
329(3)
13.1.1 Multivariate Spatial Functional Random Fields
329(1)
13.1.2 Functional Principal Components
330(1)
13.1.3 The Spatial Random Field of Scores
331(1)
13.2 Functional Kriging
332(4)
13.2.1 Ordinary Functional Kriging (OFK)
332(1)
13.2.2 Functional Kriging Using Scalar Simple Kriging of the Scores (FKSK)
333(1)
13.2.3 Functional Kriging Using Scalar Simple Cokriging of the Scores (FKCK)
333(3)
13.3 Functional Cokriging
336(4)
13.3.1 Cokriging with Two Functional Random Fields
336(2)
13.3.2 Cokriging with P Functional Random Fields
338(2)
13.4 Optimal Sampling Designs for Spatial Prediction of Functional Data
340(4)
13.4.1 Optimal Spatial Sampling for OFK
341(1)
13.4.2 Optimal Spatial Sampling for FKSK
341(1)
13.4.3 Optimal Spatial Sampling for FKCK
342(1)
13.4.4 Optimal Spatial Sampling for Functional Cokriging
343(1)
13.5 Real Data Analysis
344(4)
13.6 Discussion and Conclusions
348(3)
References
348(3)
Part III Spatio-Temporal Functional Data
351(73)
14 Spatio-temporal Functional Data Analysis
353(22)
Gregory Bopp
John Ensley
Piotr Kokoszka
Matthew Reimherr
14.1 Introduction
353(2)
14.2 Randomness Test
355(4)
14.3 Change-Point Test
359(3)
14.4 Separability Tests
362(3)
14.5 Trend Tests
365(4)
14.6 Spatio-Temporal Extremes
369(6)
References
373(2)
15 A Comparison of Spatiotemporal and Functional Kriging Approaches
375(28)
Joban Strandberg
Sara Sjdstedt de Luna
Jorge Mateu
15.1 Introduction
375(1)
15.2 Preliminaries
376(2)
15.3 Kriging
378(7)
15.3.1 Functional Kriging
378(1)
15.3.1.1 Ordinary Kriging for Functional Data
378(2)
15.3.1.2 Pointwise Functional Kriging
380(1)
15.3.1.3 Functional Kriging Total Model
381(1)
15.3.2 Spatiotemporal Kriging
382(2)
15.3.3 Evaluation of Kriging Methods
384(1)
15.4 A Simulation Study
385(9)
15.4.1 Separable
385(5)
15.4.2 Non-separable
390(1)
15.4.3 Nonstationary
391(3)
15.5 Application: Spatial Prediction of Temperature Curves in the Maritime Provinces of Canada
394(6)
15.6 Concluding Remarks
400(3)
References
400(3)
16 From Spatiotemporal Smoothing to Functional Spatial Regression: a Penalized Approach
403(21)
Maria Durban
Dae-Jin Lee
Maria del Carmen Aguilera Morillo
Ana M. Aguilera
16.1 Introduction
403(1)
16.2 Smoothing Spatial Data via Penalized Regression
404(3)
16.3 Penalized Smooth Mixed Models
407(2)
16.4 P-spline Smooth ANOVA Models for Spatial and Spatiotemporal data
409(4)
16.4.1 Simulation Study
411(2)
16.5 P-spline Functional Spatial Regression
413(2)
16.6 Application to Air Pollution Data
415(9)
16.6.1 Spatiotemporal Smoothing
416(1)
16.6.2 Spatial Functional Regression
416(5)
Acknowledgments
421(1)
References
421(3)
Index 424
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.