Spatial Statistics and Spatio-Temporal Data

Michael Sherman, Professor of Statistics, Texas A&M UniversityMichael Sherman has done extensive research on re-sampling methods for temporally or spatially dependent data and spatial statistics. He has published various papers in JASA, Biometrics and JRSS-B.  In 2000 he created a course in Spatial Statistics at Texas A&M University and has given over 35 invited presentations at University seminars, ASA meetings and special topic meetings.

• Preface xi1 Introduction 11.1 Stationarity 41.2 The effect of correlation in estimation and prediction 51.2.1 Estimation 51.2.2 Prediction 121.3 Texas tidal data 142 Geostatistics 212.1 A model for optimal prediction and error assessment 232.2 Optimal prediction (kriging) 252.2.1 An example: phosphorus prediction 282.2.2 An example in the power family of variogram functions 322.3 Prediction intervals 342.3.1 Predictions and prediction intervals for lognormal observations 352.4 Universal kriging 382.4.1 Optimal prediction in universal kriging 392.5 The intuition behind kriging 402.5.1 An example: the kriging weights in the phosphorus data 413 Variogram and covariance models and estimation 453.1 Empirical estimation of the variogram or covariance function 453.1.1 Robust estimation 463.1.2 Kernel smoothing 473.2 On the necessity of parametric variogram and covariance models 473.3 Covariance and variogram models 483.3.1 Spectral methods and the Matérn covariance model 513.4 Convolution methods and extensions 553.4.1 Variogram models where no covariance function exists 563.4.2 Jumps at the origin and the nugget effect 563.5 Parameter estimation for variogram and covariance models 573.5.1 Estimation with a nonconstant mean function 623.6 Prediction for the phosphorus data 633.7 Nonstationary covariance models 694 Spatial models and statistical inference 714.1 Estimation in the Gaussian case 744.1.1 A data example: model fitting for the wheat yield data 754.2 Estimation for binary spatial observations 784.2.1 Edge effects 834.2.2 Goodness of model fit 845 Isotropy 875.1 Geometric anisotropy 915.2 Other types of anisotropy 925.3 Covariance modeling under anisotropy 935.4 Detection of anisotropy: the rose plot 945.5 Parametric methods to assess isotropy 965.6 Nonparametric methods of assessing anisotropy 975.6.1 Regularly spaced data case 975.6.2 Irregularly spaced data case 1015.6.3 Choice of spatial lags for assessment of isotropy 1045.6.4 Test statistics 1055.6.5 Numerical results 1075.7 Assessment of isotropy for general sampling designs 1115.7.1 A stochastic sampling design 1115.7.2 Covariogram estimation and asymptotic properties 1125.7.3 Testing for spatial isotropy 1135.7.4 Numerical results for general spatial designs 1155.7.5 Effect of bandwidth and block size choice 1175.8 An assessment of isotropy for the longleaf pine sizes 1206 Space–time data 1236.1 Space–time observations 1236.2 Spatio-temporal stationarity and spatio-temporal prediction 1246.3 Empirical estimation of the variogram, covariance models, and estimation 1256.3.1 Space–time symmetry and separability 1266.4 Spatio-temporal covariance models 1276.4.1 Nonseparable space–time covariance models 1286.5 Space–time models 1306.6 Parametric methods of assessing full symmetry and space–time separability 1326.7 Nonparametric methods of assessing full symmetry and space–time separability 1336.7.1 Irish wind data 1396.7.2 Pacific Ocean wind data 1416.7.3 Numerical experiments based on the Irish wind data 1426.7.4 Numerical experiments on the test for separability for data on a grid 1446.7.5 Taylor’s hypothesis 1456.8 Nonstationary space–time covariance models 1477 Spatial point patterns 1497.1 The Poisson process and spatial randomness 1507.2 Inhibition models 1567.3 Clustered models 1588 Isotropy for spatial point patterns 1678.1 Some large sample results 1698.2 A test for isotropy 1708.3 Practical issues 1718.4 Numerical results 1738.4.1 Poisson cluster processes 1738.4.2 Simple inhibition processes 1768.5 An application to leukemia data 1779 Multivariate spatial and spatio-temporal models 1819.1 Cokriging 1839.2 An alternative to cokriging 1869.2.1 Statistical model 1879.2.2 Model fitting 1889.2.3 Prediction 1919.2.4 Validation 1929.3 Multivariate covariance functions 1949.3.1 Variogram function or covariance function? 1959.3.2 Intrinsic correlation, separable models 1969.3.3 Coregionalization and kernel convolution models 1979.4 Testing and assessing intrinsic correlation 1989.4.1 Testing procedures for intrinsic correlation and symmetry 2019.4.2 Determining the order of a linear model of coregionalization 2029.4.3 Covariance estimation 2049.5 Numerical experiments 2059.5.1 Symmetry 2059.5.2 Intrinsic correlation 2079.5.3 Linear model of coregionalization 2099.6 A data application to pollutants 2099.7 Discussion 21310 Resampling for correlated observations 21510.1 Independent observations 21810.1.1 U-statistics 21810.1.2 The jackknife 22010.1.3 The bootstrap 22110.2 Other data structures 22410.3 Model-based bootstrap 22510.3.1 Regression 22510.3.2 Time series: autoregressive models 22710.4 Model-free resampling methods 22810.4.1 Resampling for stationary dependent observations 23010.4.2 Block bootstrap 23210.4.3 Block jackknife 23310.4.4 A numerical experiment 23310.5 Spatial resampling 23610.5.1 Model-based resampling 23710.5.2 Monte Carlo maximum likelihood 23810.6 Model-free spatial resampling 24010.6.1 A spatial numerical experiment 24410.6.2 Spatial bootstrap 24610.7 Unequally spaced observations 246Bibliography 251Index 263