Geostatistical Analysis of Compositional Data
1. Introduction. 2. Regionalized Compositions. 3. Spatial Covariance Structure. 4. Concepts of Null Correlation. 5. Cokriging. 6. Practical Aspects of Compositional Data Analysis. 7. Application to Real Data. Summary and Prospects. References. Index
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additive logistic normal Aitchison 1986 Aitchison distance alr cross-covariance alr transformed alr(Z analogous arithmetic mean autocorrelation autocovariance back transformed basis space components compositional data compositional Mahalanobis concepts confidence interval confidence regions coregionalization correlogram maps correlograms corresponding covariance matrix cross-correlation over H cross-covariance matrix cross-validation errors data set defined definition Descriptive statistics Easting lag Euclidean distance expected values Figure Gaussian geostatistics h e H intrinsic spatial covariance Journel kriging and ordinary lag h logistic normal distribution lognormal cokriging estimator lognormal distribution logratio Lyons West measured multivariate normal distribution nonregionalized null ln cross-correlation obtained Olea ordinary cokriging ordinary kriging parameters proof Q-Q plot r-basis r-composition Z(u random variable random vector real space regionalized compositions sample space second-order stationary simplex ſix spatial covariance structure system of equations tion u e Q univariate vector of expected vector random function X(uo zero