Advanced Spatial Statistics: Special Topics in the Exploration of Quantitative Spatial Data Series

In recent years there has been a growing interest in and concern for the development of a sound spatial statistical body of theory. This work has been undertaken by geographers, statisticians, regional scientists, econometricians, and others (e. g. , sociologists). It has led to the publication of a number of books, including Cliff and Ord's Spatial Processes (1981), Bartlett's The Statistical Analysis of Spatial Pattern (1975), Ripley's Spatial Statistics (1981), Paelinck and Klaassen's Spatial Economet~ics (1979), Ahuja and Schachter's Pattern Models (1983), and Upton and Fingleton's Spatial Data Analysis by Example (1985). The first of these books presents a useful introduction to the topic of spatial autocorrelation, focusing on autocorrelation indices and their sampling distributions. The second of these books is quite brief, but nevertheless furnishes an eloquent introduction to the rela­ tionship between spatial autoregressive and two-dimensional spectral models. Ripley's book virtually ignores autoregressive and trend surface modelling, and focuses almost solely on point pattern analysis. Paelinck and Klaassen's book closely follows an econometric textbook format, and as a result overlooks much of the important material necessary for successful spatial data analy­ sis. It almost exclusively addresses distance and gravity models, with some treatment of autoregressive modelling. Pattern Models supplements Cliff and Ord's book, which in combination provide a good introduction to spatial data analysis. Its basic limitation is a preoccupation with the geometry of planar patterns, and hence is very narrow in scope.

Table of Contents:
1. Introduction to spatial statistics and data handling.- 1.1. A brief historical background.- 1.2. The principal problem of spatial statistics.- 1.3. Spatial sampling perspectives.- 1.4. Models of spatial autocorrelation.- 1.5. Towards a theory of spatial statistics.- 1.6 References.- Appendix 1A: Derivation of the expected value of MC.- Appendix 1B: Derivation of the expected value of GR.- 2. Developing a theory of spatial statistics.- 2.1. The small sample size problem.- 2.2. Finite versus infinite surfaces.- 2.3. Data transformations.- 2.4. Multivariate analysis.- 2.5. Higher order autoregressive models.- 2.6. Concluding comments.- 2.7. References.- 3. Areal unit configuration and locational information.- 3.1. Planar tessellations.- 3.2. Eigenfunction analysis of areal unit configuration tessellations.- 3.3. Selected applications of the principal eigenfunctions of matrix C.- 3.4. The modifiable areal unit problem.- 3.5. The importance of configurational information: a case study of Toronto.- 3.6. Implications.- 3.7. References.- 4. Reformulating classical linear statistical models.- 4.1. Autocorrelated errors models.- 4.2. Autocorrelated bivariate models.- 4.3. A spatially adjusted ANOVA model.- 4.4. The two-groups discriminant function model.- 4.5. Hypothesis testing and spatial dependence.- 4.6. Efficiency of spatial statistics estimators.- 4.7. Consistency of spatial statistics estimators.- 4.8. Conclusions.- 4.9. References.- 5. Spatial autocorrelation and spectral analysis.- 5.1. A brief background for spectral analysis.- 5.2. Relationships between autoregressive and spectral models.- 5.3. Defining the covariance matrix of a conditional spatial model using the spectral density function.- 5.4. Spectral analysis and two-dimensional shape measurement.- 5.5. Concluding comments.- 5.6. References.- 6. The missing data problem of a two-dimensional surface.- 6.1. The incomplete data problem statement.- 6.2. Background.- 6.3. Solutions available in commercial statistical packages.- 6.4. The spatial data problem.- 6.5. Properties of the conditional model when data are incomplete.- 6.6. An algorithm for the conditional spatial case.- 6.7. Constrained MLEs.- 6.8. Concluding comments.- 6.9. References.- Appendix 6A: FORTRAN subroutine.- 7. Correcting for edge effects in spatial statistical analyses.- 7.1. Problem statement.- 7.2. Major proposed solutions.- 7.3. An evaluation of the major proposed solutions.- 7.4. Conclusions and implications.- 7.5. References.- 8. Multivariate models of spatial dependence.- 8.1. A multivariate normal probability density function with spatial autocorrelation.- 8.2. Discerning latent structure in multivariate spatial data.- 8.3. Estimation problems.- 8.4. Selected empirical examples.- 8.5. Extensions to multivariate models in general.- 8.6. Concluding comments.- 8.7. References.- Appendix 8A: Rules for Kronecker products.- 9: Simulation experimentation in spatial analysis.- 9.1. Testing a null hypothesis of zero spatial autocorrelation.- 9.2. Generating autocorrelated pseudo-random numbers for two-dimensional surfaces.- 9.3. Background.- 9.4. Quality of the pseudo-random numbers.- 9.5. Variance reduction techniques.- 9.6. Selecting the number of replications r.- 9.7. Analysis of the simulation results for Chapter 6.- 9.8. Concluding comments.- 9.9. References.- 10. Summary and conclusions.- 10.1. Summary.- 10.2 Conclusions.- 10.3 References.