Geostatistical functional data analysis / edited by Jorge Mateu, Ramon Giraldo.

Format:

Book

Contributor:

Mateu, Jorge, editor.

Giraldo, Ramon, editor.

Series:

Wiley series in probability and statistics.

Wiley series in probability and statistics

Language:

English

Subjects (All):

Functional analysis.

Kriging.

Spatial analysis (Statistics).

Geology--Statistical methods.

Geology.

Physical Description:

1 online resource (451 pages) : illustrations.

Place of Publication:

Hoboken, New Jersey : Wiley, [2021]

Summary:

Spatial functional data (SFD) arises when we have functional data (curves or images) at each one of the several sites or areas of a region. Statistics for SFD is concerned with the application of methods for modeling this type of data. All the fields of spatial statistics (point patterns, areal data and geostatistics) have been adapted to the study of SFD. For example, in point patterns analysis, the functional mark correlation function is proposed as a counterpart of the mark correlation function; in areal data, analysis of a functional areal dataset consisting of population pyramids for 38 neighborhoods in Barcelona (Spain) has been proposed; and in geostatistical analysis diverse approaches for kriging of functional data have been given. In the last few years, some alternatives have been adapted for considering models for SFD, where the estimation of the spatial correlation is of interest. When a functional variable is measured in sites of a region, i.e. when there is a realisation of a functional random field (spatial functional stochastic process), it is important to test for significant spatial autocorrelation and study this correlation if present. Assessing whether SFD are or are not spatially correlated allows us to properly formulate a functional model. However, searching in the literature, it is clear that amongst the several categories of spatial functional methods, functional geostatistics has been much more developed considering both new methodological approaches and analysis of a wide range of case studies covering a wealth of varied fields of applications.

Contents:

Foreword

Chapter 1 Introduction to Geostatistical Functional Data Analysis

1.1 Spatial Statistics

1.2 Spatial Geostatistics

1.2.1 Regionalized Variables

1.2.2 Random Functions

1.2.3 Stationarity and Intrinsic Hypothesis

1.3 Spatiotemporal Geostatistics

1.3.1 Relevant Spatiotemporal Concepts

1.3.2 Spatiotemporal Kriging

1.3.3 Spatiotemporal Covariance Models

1.4 Functional Data Analysis in Brief

References

Part I Mathematical and Statistical Foundations

Chapter 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

2.3.1 Ordinary and Universal Kriging in Hilbert Spaces

2.3.2 Estimating the Drift

2.3.3 An Example: Trace‐Variogram in Sobolev Spaces

2.3.4 An Application to Nonstationary Prediction of Temperatures Profiles

2.4 An Operatorial Viewpoint to Kriging

2.5 Kriging for Manifold‐Valued Random Fields

2.5.1 Residual Kriging

2.5.2 An Application to Positive Definite Matrices

2.5.3 Validity of the Local Tangent Space Approximation

2.6 Conclusion and Further Research

Chapter 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

3.5.1 Drift Selection

3.6 Uncertainty Evaluation

3.7 Implementation Details in R

3.7.1 Example: Air Pollution Data

3.8 Conclusions

References.

Chapter 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

4.2.1 Karhunen-Loève Decomposition

4.2.2 Dealing with a Sample

4.3 Functional Kriging in a Nutshell

4.3.1 Solution Based on Basis Functions

4.3.2 Estimation of Spatial Covariances

4.4 An Example with the Precipitation Observations

4.4.1 Fitting Variogram Model

4.4.2 Making Prediction

4.5 Functional Principal Component Kriging

4.6 Multivariate Kriging with Functional Data

4.6.1 Multivariate FPCA

4.6.2 MFPCA Displays

4.6.3 Multivariate Functional Principal Component Kriging

4.6.4 Mixing Temperature and Precipitation Curves

4.7 Discussion

4.A.1 Computation of the Kriging Variance

Chapter 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

5.4.1 Model Description

5.4.2 Data Preprocessing

5.4.3 An Example of Application

5.4.4 Uncertainty Assessment

5.5 Analyzing Nonstationary Fields of FCs

5.6 Conclusions and Perspectives

Chapter 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

6.1.1 Features of Density Functions as Compositional Functional Data

6.1.2 Features of Density Functions as Distributional Data

6.2 Measures of Spatial Association for Georeferenced Density Functions.

6.2.1 Identification of Spatial Clusters by Spatial Association Measures for Density Functions

6.3 Real Data Analysis

6.3.1 The SDA Distributional Approach

6.3.2 The Compositional-Functional Approach

6.3.3 Discussion

6.4 Conclusion

Acknowledgments

Part II Statistical Techniques for Spatially Correlated Functional Data

Chapter 7 Clustering Spatial Functional Data

7.1 Introduction

7.2 Model‐Based Clustering for Spatial Functional Data

7.2.1 The Expectation-Maximization (EM) Algorithm

7.2.1.1 E Step

7.2.1.2 M Step

7.2.2 Model Selection

7.3 Descendant Hierarchical Classification (HC) Based on Centrality Methods

7.3.1 Methodology

7.4 Application

7.4.1 Model‐Based Clustering

7.4.2 Hierarchical Classification

7.5 Conclusion

Chapter 8 Nonparametric Statistical Analysis of Spatially Distributed Functional Data

8.1 Introduction

8.2 Large Sample Properties

8.2.1 Uniform Almost Complete Convergence

8.3 Prediction

8.4 Numerical Results

8.4.1 Bandwidth Selection Procedure

8.4.2 Simulation Study

8.5 Conclusion

8.A.1 Some Preliminary Results for the Proofs

8.A.2 Proofs

8.A.2.1 Proof of Theorem 8.1

8.A.2.2 Proof of Lemma A.3

8.A.2.3 Proof of Lemma A.4

8.A.2.4 Proof of Lemma A.5

8.A.2.5 Proof of Lemma A.6

8.A.2.6 Proof of Theorem 8.2

Chapter 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

9.2.1 Data Preprocessing

9.3 The Bagging Voronoi Strategy

9.4 Bagging Voronoi Clustering (BVClu)

9.4.1 BVClu of the Telecom Data

9.4.1.1 Setting the BVClu Parameters

9.4.1.2 Results

9.5 Bagging Voronoi Dimensional Reduction (BVDim)

9.5.1 BVDim of the Telecom Data.

9.5.1.1 Setting the BVDim Parameters

9.5.1.2 Results

9.6 Bagging Voronoi Regression (BVReg)

9.6.1 Covariate Information: The DUSAF Data

9.6.2 BVReg of the Telecom Data

9.6.2.1 Setting the BVReg Parameters

9.6.2.2 Results

9.7 Conclusions and Discussion

Chapter 10 Nonparametric Inference for Spatiotemporal Data Based on Local Null Hypothesis Testing for Functional Data

10.1 Introduction

10.2 Methodology

10.2.1 Comparing Means of Two Functional Populations

10.2.2 Extensions

10.2.2.1 Multiway FANOVA

10.3 Data Analysis

10.4 Conclusion and Future Works

Chapter 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

11.2.1 A Separable Spatiotemporal Basis System

11.2.2 Discretization of the Penalized Sum‐of‐Square Error Functional

11.2.3 Properties of the Estimators

11.2.4 Model Without Covariates

11.2.5 An Alternative Formulation of the Model

11.3 Simulation Studies

11.4 An Illustrative Example: Study of the Waste Production in Venice Province

11.4.1 The Venice Waste Dataset

11.4.2 Analysis of Venice Waste Data by Spatial Regression with Differential Regularization

11.5 Model Extensions

Chapter 12 Quasi‐maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models

12.1 Introduction

12.2 Model

12.2.1 Truncated Conditional Likelihood Method

12.3 Results and Assumptions

12.4 Numerical Experiments

12.4.1 Monte Carlo Simulations

12.4.2 Real Data Application

12.5 Conclusion

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

13.1 Background.

13.1.1 Multivariate Spatial Functional Random Fields

13.1.2 Functional Principal Components

13.1.3 The Spatial Random Field of Scores

13.2 Functional Kriging

13.2.1 Ordinary Functional Kriging (OFK)

13.2.2 Functional Kriging Using Scalar Simple Kriging of the Scores (FKSK)

13.2.3 Functional Kriging Using Scalar Simple Cokriging of the Scores (FKCK)

13.3 Functional Cokriging

13.3.1 Cokriging with Two Functional Random Fields

13.3.2 Cokriging with P Functional Random Fields

13.4 Optimal Sampling Designs for Spatial Prediction of Functional Data

13.4.1 Optimal Spatial Sampling for OFK

13.4.2 Optimal Spatial Sampling for FKSK

13.4.3 Optimal Spatial Sampling for FKCK

13.4.4 Optimal Spatial Sampling for Functional Cokriging

13.5 Real Data Analysis

13.6 Discussion and Conclusions

Part III Spatio-Temporal Functional Data

Chapter 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

Chapter 15 A Comparison of Spatiotemporal and Functional Kriging Approaches

15.1 Introduction

15.2 Preliminaries

15.3 Kriging

15.3.1 Functional Kriging

15.3.1.1 Ordinary Kriging for Functional Data

15.3.1.2 Pointwise Functional Kriging

15.3.1.3 Functional Kriging Total Model

15.3.2 Spatiotemporal Kriging

15.3.3 Evaluation of Kriging Methods

15.4 A Simulation Study

15.4.1 Separable

15.4.2 Non‐separable

15.4.3 Nonstationary

15.5 Application: Spatial Prediction of Temperature Curves in the Maritime Provinces of Canada

15.6 Concluding Remarks

Chapter 16 From Spatiotemporal Smoothing to Functional Spatial Regression: a Penalized Approach

16.1 Introduction.

16.2 Smoothing Spatial Data via Penalized Regression.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Mateu, Jorge Geostatistical Functional Data Analysis

ISBN:

9781119387909

1119387906

9781119387916

1119387914

9781119387886

1119387884

OCLC:

1253442473