Advanced Spatial Statistics : Special Topics in the Exploration of Quantitative Spatial Data Series
by Daniel A. Griffith
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.
