Spatial Analysis. Kanti V. Mardia
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Table of Contents
1 Cover
8 Preface
9 List of Notation and Terminology
10 1 Introduction 1.1 Spatial Analysis 1.2 Presentation of the Data 1.3 Objectives 1.4 The Covariance Function and Semivariogram 1.5 Behavior of the Sample Semivariogram 1.6 Some Special Features of Spatial Analysis Exercises
11 2 Stationary Random Fields 2.1 Introduction 2.2 Second Moment Properties 2.3 Positive Definiteness and the Spectral Representation 2.4 Isotropic Stationary Random Fields 2.5 Construction of Stationary Covariance Functions 2.6 Matérn Scheme 2.7 Other Examples of Isotropic Stationary Covariance Functions 2.8 Construction of Nonstationary Random Fields 2.9 Smoothness 2.10 Regularization 2.11 Lattice Random Fields 2.12 Torus Models 2.13 Long‐range Correlation 2.14 Simulation Exercises
12
3 Intrinsic and Generalized Random Fields
3.1 Introduction
3.2 Intrinsic Random Fields of Order 
13
4 Autoregression and Related Models
4.1 Introduction
4.2 Background
4.3 Moving Averages
4.4 Finite Symmetric Neighborhoods of the Origin in 
14 5 Estimation of Spatial Structure 5.1 Introduction 5.2 Patterns of Behavior 5.3 Preliminaries 5.4 Exploratory and Graphical Methods 5.5 Maximum Likelihood for Stationary Models 5.6 Parameterization Issues for the Matérn Scheme 5.7 Maximum Likelihood Examples for Stationary Models 5.8 Restricted Maximum Likelihood (REML) 5.9 Vecchia's Composite Likelihood 5.10 REML Revisited with Composite Likelihood