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Volume 19 Issue 1
Feb 2008
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R Tolosana-Delgado, V Pawlowsky-Glahn, J J Egozcue. Simplicial Indicator Kriging. Journal of Earth Science, 2008, 19(1): 65-71.
Citation: R Tolosana-Delgado, V Pawlowsky-Glahn, J J Egozcue. Simplicial Indicator Kriging. Journal of Earth Science, 2008, 19(1): 65-71.

Simplicial Indicator Kriging

Funds:

the Dirección General de Ensen ~ anza Superior, Ministerió de Educación y Cultura (Spain) BFM2003-05640

the Dirección General de Ensen ~ anza Superior, Ministerió de Educación y Cultura (Spain) MTM2006-03040

the Universitat de Girona (Spain) BR01/03

the Deutsche Akademische Austauschdienst (Germany) A/04/33586

More Information
  • Indicator kriging (IK) is a spatial interpolation technique devised for estimating a conditional cumulative distribution function at an unsampled location. The result is a discrete approximation, and its corresponding estimated probability density function can be viewed as a composition in the simplex. This fact suggested a compositional approach to IK which, by construction, avoids all its standard drawbacks (negative predictions, not-ordered or larger than one). Here, a simple algorithm to develop the procedure is presented.

     

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  • Aitchison, J., 1986. The Statistical Analysis of Compositional Data: Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London, UK (Reprinted in 2003 with Additional Material by the Blackburn Press)
    Billheimer, D., Guttorp, P., Fagan, W., 2001. Statistical Interpretation of Species Composition. Journal of the American Statistical Association, 96: 1205–1214 doi: 10.1198/016214501753381850
    Bogaert, P., 1999. On the Optimal Estimation of the Cumulative Distribution Function in Presence of Spatial Dependence. Mathematical Geology, 31(2): 213–239
    Bogaert, P., 2002. Spatial Prediction of Categorical Variables: The Bayesian Maximum Entropy Approach. Stochastic Environmental Research and Risk Assessment, 16: 425–448 doi: 10.1007/s00477-002-0114-4
    Carle, S., Fogg, G., 1996. Transition Probability-Based Indicator Geostatistics. Math. Geol. , 28: 453–476 doi: 10.1007/BF02083656
    Carr, J. R., 1994. Order Relation Correction Experiments for Probability Kriging. Math. Geol. , 26: 605–621 doi: 10.1007/BF02089244
    Carr, J. R., Mao, N. H., 1993. A General-Form of Probability Kriging for Estimation of the Indicator and Uniform Transforms. Math. Geol. , 25: 425–438 doi: 10.1007/BF00894777
    Christakos, G., 1990. A Bayesian/Maximum Entropy View to the Spatial Estimation Problem. Math. Geol. , 22: 763–777 doi: 10.1007/BF00890661
    Eaton, M. L., 1983. Multivariate Statistics: A Vector Space Approach. John Wiley & Sons, New York
    Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., et al., 2003. Isometric Logratio Transformations for Compositional Data Analysis. Math. Geol. , 35: 279–300 doi: 10.1023/A:1023818214614
    Journel, A. G., 1983. Nonparametric Estimation of Spatial Distributions. Math. Geol. , 15: 445–468 doi: 10.1007/BF01031292
    Juang, K. W., Lee, D. Y., Hhsiao, C. K., 1998. Kriging with Cumulative Distribution Function of Order Statistics for Delineation of Heavy-Metal Contaminated Soils. Soil Science, 163: 797–804 doi: 10.1097/00010694-199810000-00003
    Martín-Fernández, J. A., Barceló-Vidal, C., Pawlowsky-Glahn, V., 2000. Zero Replacement in Compositional Data Sets. In: Kiers, H., Rasson, J., Groenen, P., et al., eds., Studies in Classification, Data Analysis, and Knowledge Organization—Proceedings of the 7th Conference of the International Federation of Classification Societies (IFCS'2000). Springer Verlag, Berlin. 155–160
    Mateu-Figueras, G., Pawlowsky-Glahn, V., Barceló-Vidal, C., 2003. Distributions on the Simplex. In: Thió-Henestrosa, S., Martín-Fernández, J. A., eds., The First Compositional Data Analysis Workshop, Proceedings of CODAWORK'03, October 15–17, Universitat de Girona, ISBN 84-8458-111-X
    Matheron, G., 1976. A Simple Substitute for the Conditional Expectation: The Disjunctive Kriging. In: Guarascio, M., David, M., Huijbregts, C., eds., Advanced Geostatistics in the Mining Industry. D. Reidel Publishing Company, Dordrecht. 221–236
    Pardo-Igúzquiza, E., Dowd, P. A., 2005. Multiple Indicator Cokriging with Application to Optimal Sampling for Environmental Monitoring. Computers and Geosciences, 31: 1–13 doi: 10.1016/j.cageo.2004.08.006
    Pawlowsky, V., 1989. Cokriging of Regionalized Compositions. Math. Geol. , 21(5): 513–521 doi: 10.1007/BF00894666
    Pawlowsky-Glahn, V., 2003. Statistical Modelling on Coordinates. In: Thió-Henestrosa, S., Martín-Fernández, J. A., eds., The First Compositional Data Analysis Workshop, Proceedings of CODAWORK'03, October 15–17, Universitat de Girona, ISBN 84-8458-111-X
    Pawlowsky-Glahn, V., Egozcue, J. J., 2001. Geometric Approach to Statistical Analysis on the Simplex. Stochastic Environmental Research and Risk Assessment, 15: 384–398 doi: 10.1007/s004770100077
    Pawlowsky-Glahn, V., Egozcue, J. J., 2002. BLU Estimators and Compositional Data. Math. Geol. , 34: 259–274 doi: 10.1023/A:1014890722372
    Pawlowsky-Glahn, V., Olea, R., 2004. Geostatistical Analysis of Compositional Data. Oxford University Press, Oxford
    Simonoff, J., 2003. Analyzing Categorical Data. Springer Verlag, New York. 248–250
    Sullivan, J., 1984. Conditional Recovery Estimation through Probability Kriging—Theory and Practice. In: Geostatistics for Natural Resources Characterization. NATO ASI Series, Series C: Mathematical and Physical Sciences, 122: 365–384
    Suro-Pérez, V., Journel, A. G., 1991. Indicator Principal Component Kriging. Math. Geol. , 23(5): 759–788 doi: 10.1007/BF02082535
    Tolosana-Delgado, R., 2006. Geostatistics for Constrained Variables: Positive Data, Compositions and Probabilities—Application to Environmental Hazard Monitoring: [Dissertation]. Medi Ambient-Física i Tecnologia Ambientals, Universitat de Girona
    Tolosana-Delgado, R., Pawlowsky-Glahn, V., Egozcue, J. J., 2008. Indicator Kriging without Order Relation Violations. Math. Geol. (in Press)
    Vargas-Guzmán, J. A., Dimitrakopoulos, R., 2003. Successive Nonparametric Estimation of Conditional Distributions. Math. Geol. , 35: 39–52 doi: 10.1023/A:1022361028297
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